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FIRST    BOOK 


AEITHMETIC, 


INCLUDING 


OEAL  AND  WRITTEN  EXEECISES. 


BY  DANIEL  W.   FISH,   A.M., 

EDITOR  OF  ROBINSON'S  SERIES  OF  PROGRESSIVE  ARITHMETICS. 


IVISON,  BLAKEMAN,  TAYLOR  &  CO., 

NEW  YORK   AND   CHICAGO. 

1878 


GHORTER  COURSE. 


FIRST  BOC   '  IN  ARITHMETIC.     PRIMARY.         £ 
COMPLE TE  .  -RITHME TIC.     In  One  volume* 
COMPLETE  ALGEBRA. 

ARITHMETICAL  PROBLEMS.    ORAL  and  WRITTEN. 
ALGEBRAIC  PROBLEMS. 

KE  YS  to  COMPLETE  ARITHMETIC  and  PROBLEMS,  and 

to  COMPLETE  ALGEBRA  and  PROBLEMS, 

in  separate  volumes,  for  Teachers. 


Arithmetic,  on  AT,  and  WRITTEN,  usually  taught 
in  THREE  books,  is  now  offered,  complete  and 
thorough,  in  ONE  book,  "  THE  COMPLETE  ARITHMETIC." 


*  This  COMPLETE  ARITHMETIC  is  also  published  in  TWO  VOLUMES.     TAUT  J. 
and  PART  II.  are  each  bound  separately ,  in  CLOTH. 


Copyright,  1874,  by  DANIEL  W.  FISH. 


Eiectrotyped  by  SMITH  &  McDoucAL,  82  Beekman  St.,  N.  Y. 


A  RITHMETIC  has  been  defined  as  "the  science  of  numbers,  and 
J-^-  the  art  of  computing  by  means  of  them."  It  embraces, 

1st.  The  mode  of  representing  numbers  by  figures  and  signs,  in 
accordance  with  an  accepted  system  ; 

2d.  The  principles  and  methods  of  their  combination  in  addition, 
subtraction,  multiplication,  and  division  ;  and, 

3d.  The  application  of  these  principles  and  methods  to  the  solu- 
tion of  practical  problems. 

Primary  Arithmetic  can  do  little  more  than  put  the  pupil  in  pos- 
session of  the  alphabet  of  numbers,  and  make  him  familiar  with 
the  various  tables,  securing  readiness  and  accuracy  in  their  use, 
and  neatness  and  skill  in  written  exercises  upon  them. 

In  this  book,  the  object  has  been  to  secure  this  end  by  easy, 
gradual,  and  national  steps,  and  in  such  a  familiar  manner,  as  to 
avoid  the  drudgery  of  memorizing  the  abstract  tables,  and  at  the 
same  time  inspire  :""  Diligent  thought  in  regard  to  the  more  simple 
processes  that  involve  the  use  of  numbers. 

The  plan  of  this  book  is  unique,  and  it  is  believed  that  it  will 
supply  a  want  long  felt  by  primary-school  teachers.  The*  natural 
and  orderly  development  of  the  subject,  the  systematic  arrangement, 
the  copious  illustrative  exercises,  and  the  provision  for  exhaustive 
drill  exercises,  cannot  fail  to  meet  the  views  of  the  most  thorough 
and  exacting  teacher,  and,  at  the  same  time,  interest  and  attract 
the  pupil. 

The  first  seventeen  lessons  are  intended  to  present  the  numbers 
from  one  to  ten,  inclusive,  as  numbers,  in  such  manner  that  each  of 
them  shall  be  intelligently  apprehended,  not  merely  as  a  name> 
but  as  an  IDEA — what  it  is,  how  it  is  represented,  and  what  is  its 
value  relative  to  each  of  the  others. 

fi  r^  7  1 : 


IV  PREFACE. 

Succeeding  this  are  familiar  illustrations  of  the  use  of  signs  ;  ana 
a  series  of  easy  and  progressive  exercises  present  the  various  com- 
binations that  can  be  made  by  means  of  any  two  of  all  the  numbers 
under  12 — giving  practical  drill  exercises  on  the  tables,  and  illus- 
trating their  use  by  means  of  problems. 

A  new  form  of  table,  "equal  parts  of  numbers"  has  been  intro- 
duced and  practically  applied,  consistent  with  primary  operations 
upon  whole  numbers,  naturally  deduced  from  the  multiplication 
table  as  is  the  ordinary  table  of  division.  The  practical  value  of 
this  will  be  apparent  from  the  problems  and  examples  given  in 
illustration,  and  the  drill  exercises  in  connection  with  it. 

The  exercises  in  notation  and  numeration  are  simple  and  pro- 
gressive,  and  may  be  further  extended,  at  the  option  of  the  teacher. 

The  latter  part  of  the  book  makes  a  more  thorough,  but  still  pro- 
gressive and  systematic,  presentation  of  principles  and  methods  in 
the  fundamental  ruleaj  oral  and  written. 

The  simple  exercises  here  presented  in  Fractions  and  Measures 
(Denominate  Tables)  will  furnish  opportunity  for  more  extended 
exercises,  such  as  the  judicious  teacher  may  desire,  or  the  require- 
ments of  particular  classes  may  demand. 

The  Pictot^al  Illustrations,  designed  more  for  use  than  ornament, 
will  commend  themselves  to  the  taste  and  judgment  of  discrimi- 
nating teachers. 

In  the  preparation  of  this  book,  the  author  has  kept  constantly 
in  view  such  a  systematic  arrangement  and  development  of  prin- 
ciples and  methods  as  to  present  the  subject  in  the  most  natural  as 
well  as  the  most  comprehensive  manner. 

The  author  desires  to  make  special  acknowledgment  of  the  valu- 
able services  rendered  in  the  plan,  arrangement,  and  compilation 
of  this  book,  by  James  Cruikshank,  LL.D.,  a  gentleman  well  known 
fco  the  educational  world,  whose  large  experience  for  a  number  of 
years  as  Superintendent  of  the  Primary  Schools  of  the  city  of 
Brooklyn  has  made  him  familiar  with  the  needs  of  teachers 
of  this  grade  of  schools. 

With  a  desire  to  contribute  to  the  facilities  for  elementary  in- 
struction, this  little  work  is  confidently  submitted  to  the  public. 

D.  w!  F. 

BROOKLYN,  April,  1875. 


HINTS  TO  r  'EACHERS 


rpHE  division  of  this  book  into  lessons  is  not  at  all  intended  to 
-*-  mark  out  the  limit  of  the  daily  exercises.  Each  lesson  dis- 
cusses a  separate  topic,  and  many  of  them  furnish  or  suggest  mat- 
ter upon  which  several  days  may  be  profitably  spent.  Some  of 
them  present  drill  exercises  that  may  be  frequently  repeated  with 
profit — returning  to  them  from  more  advanced  periods.  Practically, 
the  exercises  embraced  in  this  book  cover  three  years  or  more  of 
the  primary  school  course  as  prescribed  in  most  of  our  city  schools. 

Advance  slowly ;  one  step  at  a  time,  and  always  secure  a  perfect 
mastery  of  any  principle  or  operation  upon  which  another  depends, 
before  proceeding  to  the  next. 

Go  over  only  so  much  ground  at  any  one  exercise  as  may  be 
thoroughly  understood,  and  review  daily. 

The  greatest  source  of  embarrassment  to  the  teacher,  and  of  dis- 
gust and  waning  interest  on  the  part  of  the  pupil,  is  found  in  the 
accumulation  of  imperfectly  mastered  lessons. 

Endeavor  to  secure  the  interest  of  the  class,  and  never  do  for  a 
pupil  what  he  can  be  readily  led  to  do  for  himself.  Slate  exercises 
are  important  from  the  first,  and  if  judiciously  conducted  can  never 
fail  to  please  and  instruct. 

The  various  combinations  by  addition,  subtraction,  multiplica- 
tion, and  division,  presented  in  the  tables,  furnish  the  instruments 
for  all  arithmetical  operations.  If  the  pupil  is  skillful  in  these,  the 
only  other  thing  needful  is  such  a  familiar  knowledge  of  the  relation 
of  things  as  to  know  what  process  should  be  used  in  the  solution  of 
problems. 

In  the  early  lessons  in  arithmetic,  the  judicious  teacher  will 
observe  that  the  introduction  of  numbers  and  of  the  successive  digits 
representing  them  should  be  gradual.  Examples  should  at  first 
contain  only  1's  and  2's  ;  then  1's,  2's,  and  3's,  until  the  pupil  can 
add  rapidly  and  correctly  in  whatever  order  they  are  combined 


ri  HINTS    TO    TEACHERS. 

Then  introduce  4's  with  the  preceding,  etc.  This  remark  applies 
also  to  subtraction,  multiplication,  etc.  In  all  cases  where  there  is 
hesitation  or  forgetfulness,  return  to  special  drill,  in  series,  to  mas- 
ter the  particular  number  upon  which  the  fault  occurs. 

The  fundamental  idea  in  all  numerical  combinations  is  found  in 
counting  in  series.  If  each  step  as  outlined  in  this  book  is  mastered 
as  indicated,  progress  will  be  easy  and  rapid,  and  the  result  most 
satisfactory. 

Thus,  in  counting  by  6's,  the  following  give  all  possible  addi- 
tions of  6  with  the  units  of  any  other  number  : 
0  +  6  +  6;  1  +  6  +  6;  2  +  6  +  6;  3  +  6  +  6;  4  +  6  +  6;  5  +  6  +  6;  6  +  6  +  6. 
Counting  back  gives  all  possible  subtractions  of  6.  Multiplication 
and  division,  through  the  limit  of  each  table  are  involved  in  count- 
ing by  6's  to  72  ;  as,  6,  12,  18,  24,  30,  36,  42,  48,  54,  60,  66,  72,  and 
similarly  for  other  tables.  Observe  carefully  the  models  under  the 
several  lessons. 

At  each  step,  as  the  pupil  becomes  familiar  with  the  formal  oper- 
ation of  summing  the  series,  he  should  be  led  to  observe  and  state 
how  many  times  the  recurring  number  has  been  used  ;  thus,  6, 12, 
18  (6  +  6  +  6)  ;  there  are  3  sixes  in  18,  or  3  times  6  are  18,  etc. 

Little  real  progress  can  be  made  even  in  memorizing  until  the 
name  of  each  of  the  digits  becomes  to  the  pupil  an  intelligible  sign 
of  the  number  for  which  it  stands.  Thus,  the  figure  5,  or  the  name 
five,  should,  upon  being  seen  or  heard,  as  clearly  recall  the  idea 
of  5  units,  singly,  and  together,  as  any  common  word  brings  up  to 
the  mind  the  idea  which  it  represents. 

Care  should  be  taken  that  the  eye,  as  well  as  the  ear,  be  addressed 
and  cultivated.  Skillful  oral  repetition  of  the  tables  does  not 
necessarily  produ'ce  rapid  and  correct  results,  when  the  pupil  has 
need  to  perform  operations  silently.  This  is  an  important  consid- 
eration, inasmuch  as  the  practical  use  of  arithmetic  is  not  oral,  but 
mental,  and  the  eye  and  the  hand,  rather  than  the  ear  and  the 
tongue,  become  the  instruments. 

BLACKBOARD  DRILL. — The  blackboard  should  be  a  constant 
accessory  in  school-room  instruction.  A  few  among  the  many 
methods  which  should  be  used  from  time  to  time  are  suggested  : 

1.  An  exercise  having  been  written  upon  the  board,  let  a  pupil, 
as  called  upon,  go  through  the  exercise  as  rapidly  as  is  consistent 


HIKTS     TO     TEACHERS.  HI 

with  accuracy,  pupils  or  teacher  indicating  errors  in  such  a  way  as 
may  be  deemed  expedient.  Generally  the  pupil  should  be  required 
to  correct  the  error  himself,  when  attention  is  called  to  it.  Another 
may  then  take  up  the  work,  and  so  on. 

2.  Proceed  as  before,  except  that  each  pupil  in  turn  should  name 
one  step  or  result,  and  any  error  being  made,  the  next  should  correct 
it,  or,  failing  to  do  so,  any  member  of  the  class  may  raise  his  hand, 
and  make  the  correction.     No  blunder  should  be  allowed  to  pass 
unnoticed. 

It  is  generally  advisable  that  each  class  exercise  illustrated  upon 
the  board  be  also  made  a  slate  exercise  for  silent  work. 

3.  When  a  little  familiarity  with  any  class  of  exercises  is  secured, 
the  pupils  should  be  encouraged  to  do  the  work  upon  the  black- 
board themselves,  without  the  intervention  of  the  teacher. 

4.  From  the  very  first  no  carelessness  or  slovenliness  in  making 
figures,  or  in  the  general  form  of  the  written  exercises  should  ever, 
under  any  pretense,  be  allowed.     Time  spent  in  securing  neatness 
will  be  regained  tenfold  in  the  pupils'  subsequent  progress,  and 
in  the  culture  in  which  it  will  result.     This  remark  applies  also 
to  slate  exercises.     All  slate  exercises  should  be  carefully  examined, 
aod  the  errors  pointed  out,  and  then  corrected  by  the  pupil. 

Primary  arithmetic  does  not  involve  any  complicated  processes 
of  analysis  or  of  reasoning.  It  deals  chiefly  with  facts,  and  considers 
only  the  simplest  and  most  evident  relations  of  things.  It  is, 
therefore,  recommended  that  for  mal  analyses  be  used  but  sparingly. 
Those  given  upon  pages  41,  45,  46,  and  elsewhere,  are  only  sugges- 
tive, and  after  the  process  (that  is,  the  nature  of  the  operation)  in 
any  given  case  is  understood,  they  may  be  discontinued,  or  varied, 
or  used  only  occasionally.  They  are  not  in  themselves  an  end,  but 
only  a  means  of  determining  the  operation  to  be  performed. 

It  is  recommended  that  wherever  problems  are  introduced,  the 
relations  of  the  things  to  which  they  refer  be  carefully  explained, 
and  then  the  relations  of  the  numbers  will  be  readily  understood. 

The  attention  of  the  pupils  may  be  called  to  the  several  steps 
by  judicious  questions,  and  they  may  also  be  encouraged  to  make 
problems  suited  to  numbers  given  in  any  case  ;  as,  given  5x4; 
we  may  say,  "  What  is  the  cost  of  4  yards  of  tape  at  5  cents  a 
yard  ?  "  etc. 


Till  HINTS     TO     TEACHERS. 

When  problems  involve  more  than  one  operation,  the  pupil's 
attention  should  be  called  to  the  reasons  and  necessity  for  each.  See 
example,  page  90,  Ex.  7. 

Most  of  the  lessons  may  and  should  be  very  much  extended  by 
additional  examples  and  illustrations,  always,  however,  observing 
to  keep  icithin  the  scope  and  spirit  of  the  lesson.  As,  on  page  10,  no 
exercise  must  embrace  any  number  beyond  6,  nor  any  combination 
whose  result  is  greater  than  6 ;  on  page  50,  no  result  greater  than 
36,  and  no  number  greater  than  6  used  in  producing  the  result.  In 
the  review  of  each  lesson,  all  smaller  numbers  should  be  used. 

The  exercise  on  page  46,  and  others  similar  following,  do  not 
belong  to  Fractions,  but  exhibit  a  simple  form  of  deduction  from 
multiplication ;  thus,  since  3  times  4  are  12,  it  follows  that  4  is 
contained  3  times  in  12,  and  also  that  one-third  of  12  is  4.  It  will 
be  well  generally  to  teach  these  in  connection,  as  on  page  101. 

Counting  in  series  orally,  and  as  illustrated  on  the  board,  should 
be  often  repeated,  and  many  exercises  may  be  given  besides  those 
contained  in  the  lessons. 

FRACTIONS. — No  attempt  has  been  made  in  this  book  to  do  more 
than  present  the  simplest  elementary  ideas  of  fractions.  Every 
exercise  should  be  carefully  illustrated  by  objects,  and  by  lines  or 
figures  upon  the  board. 

MEASURES. — So  far  as  practicable,  each  of  the  tables  should  be 
illustrated  by  actual  objects,  presenting  to  the  senses  the  values 
named,  and  the  relations  to  each  other  of  the  different  units.  Exer- 
cises may  be  much  extended,  so  that  intelligent  skill  shall  be 
acquired. 

Even  though  a  class,  upon  taking  up  this  book,  have  already 
acquired  some  knowledge  of  numbers,  it  will  be  found  profitable  to 
review  carefully  most  of  the  lessons  from  the  beginning,  or  at 
least  to  ascertain  that  each  pupil  is  skillful  in  the  exercises. 

In  all  oral  exercises,  so  called,  the  aim  should  be  not  to  make  the 
pupil  simply  flippant  and  ready  in  repeating  a  number  of  similar 
exercises  after  a  model  has  been  given,  for  this  often  requires  little 
or  no  thought,  and  is  practically  useless  ;  but  what  we  may  call 
mental  msion  should  be  cultivated — to  bring  before  the  mind  all 
the  numbers  and  conditions  involved,  and  arrange  or  group  them 
so  that  the  result  may  become  apparent. 


The  first  lesson  in  numbers  to  be  taught  the  child  is 
to  count.  He  cannot  learn  the  yalue  of  figures  from  1  to 
10  until  he  can  count  ten  objects. 

The  Numeral  Frame  is  one  of  the  most  convenient 
aids  in  teaching  to  count,  and  the  primary  operations  in 
the  use  of  numbers.  When  this  cannot  be  had,  a  box  of 
beans,  marbles,  or  similar  objects  may  be  used. 

Holding  up  the  frame  before  the  pupils,  move  the  balls 
on  the  first  wire,  one  at  a  time,  while  the  children  count 
one,  two,  three,  four,  five,  six,  seven,  eight,  nine,  ten. 

Then  the  exercise  may  be  extended  to  twenty,  by  moving 
the  balls  on  two  wires  ;  then  to  thirty,  by  moving  the 
balls  on  three  wires,  and  so  on  to  one  hundred. 

When  the  pupils  can  count  by  ones  to  one  hundred, 
they  may  be  taught  to  count  by  twos.  Move  two  balls 
on  one  wire,  and  two  more  on  the  next,  and  so  on,  the 
pupils  saying,  two,  four,  six,  eight,  ten,  twelve,  etc. 

When  the  pupils  can  count  by  tivos  as  far  as  fifty,  and 
have  also  learned  to  write  figures  as  far  as  twenty,  write 
a  column  of  2's  on  the  board,  and  train  them  to  add  the 
figures  in  the  same  manner  as  the  balls  were  counted. 

Next,  move  one  ball  on  the  first  wire,  and  two  balls  on 
each  succeeding  wire,  while  the  pupils  say,  one,  three, 
five,  seven,  nine,  eleven,  etc. 

After  sufficient  exercise  on  these  combinations,  require 
them  to  write  a  short  column  of  2's  on  their  slates  with 
a  1  at  the  bottom,  and  add  them  as  before,  writing  the 
sum  below  the  column. 


10  IK     A  HITH,METIC. 

When  sufficiently  drilled  &TL..iwos,  the  same  method 
may  be  pursued  in  teaching  them  to  count  by  threes. 
Thus,  three,  six,  nine,  twelve,  fifteen,  etc.  Then  com- 
mencing with  one  ;  thus,  one,  four,  seven,  ten,  thirteen,  etc. 
Then  with  two  ;  thus,  two,  five,  eight,  eleven,  fourteen,  etc. 

Follow  these  drills  with  the  same  exercises  on  the  slate 
or  board  as  with  the  2's. 

The  same  method  should  be  pursued  in  teaching  them 
to  count  and  add  by  fours,  fives,  sixes,  etc. 

At  the  same  time  that  the  pupil  is  thus  taught  to  count, 
and  to  know  figures  as  symbols,  he  should  also  be  taught 
their  value,  and  the  value  of  numbers  as  associated  with 
the  number  of  objects  counted.  He  should  be  required 
to  perform  the  same  operations  on  the  slate  or  blackboard 
with  figures  that  he  has  performed  orally  with  objects. 

The  apt  teacher,  by  a  judicious  use  of  this  frame,  may 
easily  teach  a  child  to  count  from  one  to  a  hundred,  and 
to  add,  subtract,  multiply,  and  divide  with  facility. 

The  counting  and  other  operations  should  be  done 
silently  by  the  eye,  and  results  only  given  by  the  voice. 

It  is  not  intended  to  make  a  small  work  like  this 
take  the  place  of  the  living  teacher.  The  sample  lessons 
can  contain  but  a  few  hints  and  methods  to  aid  the 
teacher  in  giving  the  pupil  something  to  do;  therefore,  the 
number  and  variety  of  the  exercises  on  each  page,  both 
for  oral  and  written  drill,  should  be  increased  as  the  cir- 
cumstances and  the  capacity  of  the  child  seem  to  require. 
The  how  and  the  why  can  be  much  better  explained  by 
the  teacher -than  by  the  author,  in  so  limited  a  space. 


One      Nest 
Two      Birds 


Three  Leaves  3  III. 
Steeples  ^  IY. 
Sheep  ff  V. 


LESSON    I. 

1  I. 

2  II. 


Boys 

Seven  Girls 
Eif/ht  Acorns 


6  VI. 

7  vii. 

8  VIII. 


Berries    9      IX. 
Posts    10     X. 


FIRST     BOOK 


LESSON    II. 

Here  is  a  picture  of  a  frame,  with  ten  wires,  and  ten 
balls  on  each  wire.     It  is  called  a  Numeral  Frame. 

1.  On  the  second  wire  at 
the  right  is  one  ball. 

One.    Written  1 

2.  How  many  balls  are 
one  ball  and  one  ball  more  ? 

Two.    Written  2 

3.  Two    balls    and    one 
ball?  Three.   Written  3 

4.  Three  balls   and  one 
ball?   Four.    Written  ^ 

5.  Four   balls   and   one 
ball?    Five.    Written  5 

6.  Five    balls    and   one 
ball?       Six.    Written  6 

7.  Six  balls  and  one  ball? 
Seven.    Written      / 

8.  Seven  balls  and  one  ball  ?    Eight.    Written     8 

9.  Eight  balls  and  one  ball  ?    Nine.       Written      9 

10.  Nine  balls  and  one  ball  ?     Ten.         Written  10 

11.  How  many  balls  on  each  wire  ?     Ten. 
12. '  Is  there  any  figure  that  stands  for  ten  ? 

13.  What  is  the  largest  number  expressed  by  one  figure  ? 

14.  What  does  1  mean  when  it  stands  alone  ? 

15.  What  does  it  mean  when  it  has  a  0  on  the  right  of  it  ? 

Figures.    0,    1,    2,    3,    4,   5,   6,    7,    8,    9. 

Naught,  One,  Two,  Three,  Fonr,  Five,  Six,  Seven,  Eight,  Nine. 


COUNTING. 


AEITHMETIC. 


13 


LESSON     III. 

1.  What  do  you  see  in  the  picture  ? 

2.  How  many  horses  ?     How  many  dogs  ? 

3.  What  is  in  the  dog's  mouth  ?     How  many  baskets  ? 

4.  Show  me  one  book.     Point  to  one  boy. 

5.  Hold  up  one  hand.     How  many  hands  have  you  ? 

6.  Hold  up  one  finger.     Hold  up  one  more. 

7.  One  finger  and  one  more  are  how  many  fingers  ? 
''8.  Two  fingers  are  how  many  more  than  one  finger  ? 

9.  One  finger  is  how  many  less  than  two  fingers  ? 

10.  How  many  ears  has  the  horse  ?  How  many,  the  dog  ? 

11.  Make  one  short  line  on  your  slate.  / 

12.  One  line  and  one  more  are  how  many  lines  ?     /  / 

13.  How  many  ones  make  two  ? 

14.  Kub  out  one  line  and  how  many  are  left  ? 

15.  Two  lines  less  one  line  are  how  many  lines  ? 

16.  What  is  a  single  thing  called  ? 

17.  Write  the  word  one  on  your  slate.  &ne. 

18.  Make  the  figure  for  one  on  your  slate.         _/. 

W.  How  many  are  one  and  one  more  ?  Two. 


FIEST     BOOK 


LESSON    IV. 

1.  How  many  girls  in  this  picture  ?   How  many  birds  ? 

2.  How  many  roses  has  one  girl  in  her  hand  ? 

8.  How  many  roses  has  the  other  in  her  apron  ? 

4.  One  bird  and  one  bird  are  how  many  birds  ? 

5.  Two  are  how  many  more  than  one  ? 

6.  How  many  ones  make  two  ? 

7.  How  many  eyes  have  you  ?    How  many  ears  ? 

8.  Hold  up  two  fingers.     Hold  up  one  more. 

9.  Make  two  short  lines  on  your  slate.  // 

10.  Make  one  more.     How  many  are  there  now  ?  //  / 

11.  Two  lines  and  one  line  are  how  many  lines  ? 

12.  One  and  two  are  how  many  ? 

13.  Two  lines  are  how  many  less  than  three  lines  ? 
H.  Three  lines  are  how  many  more  than  two  lines  ? 

15.  Eub  out  one  line  ;  how  many  are  left  ? 

16.  Rub  out  two  more  lines ;  how  many  are  left  ? 

17.  Write  the  word  two  on  your  slate.  Q/tvo. 

18.  Make  the  figure  for  tivo  on  your  slate.       2. 

19.  How  many  are  two  and  one  more  ?  Three* 


ARITHMETIC. 


15 


LESSON    V. 

1.  In  the  picture,  how  many  squirrels  ?    How  many 
bees  ?    How  many  squirrels  with  a  nut  ? 

2.  Two  squirrels  and  one  squirrel  are  how  many  ? 

3.  Three  bees  are  how  many  more  than  2  bees  ? 

4.  Three  less  one  are  how  many  ?     Three  less  2  ? 

5.  How  many  ones  make  three  ? 

6.  How  many  are  2  and  1  ?     1  and  2  ? 

7.  Make  three  short  lines  on  your  slate. 

8.  Eub  out  one  line  ;  how  many  are  left  ? 

9.  Rub  out  one  more  ;  how  many  are  left  ? 

10.  Three  less  three  are  how  many  ? 

11.  Make  three  lines  again.     Now  one  more. 

12.  Three  lines  and  one  line  are  how  many  lines  ? 

13.  Hold  up  one  finger.     Two  fingers.     Three  fingers. 

14.  Count  three.     How  many  ones  in  three  ? 

15.  How  many  2's  in  three  ?    Ans.  One  2  and  1  over. 

16.  Write  the  word  three  on  your  slate.  dffllee. 

17.  Make  the  figure  that  stands  for  three.       3. 

18.  How  many  are  three  and  one  more  ?         Four. 


Ill 


III  I 


I 
16 


FIEST     BOOK 


LESSON    VI. 

1.  How  many  birds  in  the  picture  ?    How  many  eggs  ? 

2.  How  many  are  2  birds  and  2  birds  ? 
&  How  many  ones  in  four  ? 

4.  Make  2  short  lines  ;  then  2  more.  //  // 

£  How  many  2's  in  four  ?     2  and  2  are  how  many  ? 

6.  Count  four  by  ones.     Count  four  by  2's. 

7.  Two  birds  taken  from  four  birds  leave  how  many? 

8.  Four  less  one  are  how  many  ?    Four  less  3  ? 

9.  How  many  are  3  and  1  ?     1  and  3  ? 

10.  How  many  ones  in  four  ?     How  many  2's  ? 

11.  How  many  3's  in  four  ?    Ans.  One  3  and  1  over. 

12.  Four  are  how  many  more  than  three  ?    How  many 
more  than  two  ? 

18.  How  many  eggs  must  be  taken  from  the  nest  to 

leave  1  egg  ?    How  many  to  leave  2  ?    To  leave  3  ? 

14.  Write  the  word  four  on  your  slate.  ffikut,. 

15.  Make  the  figure  that  stands  for  four.          Jf. 

16.  Count  from  4  back  to  one.     Four,  three,  two,  one. 

17.  How  many  are  four  and  one  more  ?  Five. 


ARITHMETIC. 


17 


LESSON    VII, 

1.  In  this  picture  how  many  birds  ?     How  many 
peaches  ?    How  many  birds  on  the  limb  ? 

2.  Five  birds  are  how  many  more  than  4  ?    Than  3  ? 

3.  Three  birds  and  2  birds  are  how  many  birds  ? 
^.  Two  peaches  and  3  peaches  are  how  many  ? 

5.  Five  peaches  less  3  peaches  are  how  many  ? 

6.  Five  peaches  less  2  peaches  are  how  many  ? 

7.  Two  fishes  and  how  many  more  make  five  fishes  ? 

8.  Three  fishes  and  how  many  more  make  five  ? 

9.  Make  3  short  lines.     Now  2  more.  ///  // 
10.  Three  and  2  are  how  many  ?     2  and  3  ? 

.7L  Make  4  short  lines.     Now  one  more.  III!  I 

12.  Four  and  1  are  how  many  ?     1  and  4  ? 

-7$.  If  2  birds  fly  away,  how  many  are  left  ?    If  2  more  ? 

14.  How  many  2's  in  five  ?    .4^5.  Two  2's  and  1  over. 

15.  Write  the  word^zm  (ffiwe. 

16.  Write  the  figure  that  stands  for  five.  5. 

17.  Count  five.     Count  from  five  back  to  one. 

18.  How  many  are  five  and  one  more  ?  Six. 


• 


18 


FIEST     BOOK 


LESSON    VIII. 

1.  There  are  three  boats  on  the  water  and  three  on 
the  land.     How  many  in  all  ?     3  and  3  are  how  many  ? 

2.  How  many  boys  on  the  ice  ?    How  many  2's  in  six? 

3.  Three  boats  from  six  boats  leave  how  many  boats  ? 

4.  Six  boys  are  how  many  more  than  4  boys  ? 

5.  How  many  2's  make  six  ?   How  many  3's  make  six  ? 

6.  Count  six  by  ones.     By  2's.     By  3's. 

7.  There  are  2  sails  on  1  boat ;  how  many  on  3  boats  ? 

8.  Three  2's  are  how  many  ?     Two  3's  are  how  many  ? 

9.  How  many  are  six  boats  less  5  boats  ? 

10.  Four  boats  and  how  many  more  make  six  boats  ? 

11.  Six  boys  less  2  boys  are  how  many  boys  ?    Six  boys 
less  4  boys  are  how  many  ? 

12.  Three  boats  are  how  many  less  than  six  boats  ? 

13.  Make  six  lines  by  2's.    //////     By  3's.    ////// 

14.  Write  the  word  six  on  your  slate.  <3&&. 

15.  Make  the  figure  that  stands  for  six.  6. 

16.  Count  six.     Count  from  six  back  to  one. 

17.  How  many  are  six  and  one  more.  Seven. 


IKAEITHMETIC.  19 

LESSON    IX. 

L  How  many  boats  are  2  boats  and  2  boats  ? 

2.  How  many  boys  are  2  boys,  2  boys,  and  2  boys  ? 

#.  Count  by  2's  to  4.     Count  by  2's  to  6. 

4.  How  many  2's  in  6  ?    How  many  3's  in  6  ? 

5.  Six  cents  are  how  many  more  than  3  cents  ?    How 
many  more  than  4  cents  ?     Than  2  cents  ? 

6.  Kepeat  this  table. 

1  and  5  are  6.  4  and  2  are  6. 

2  and  4  are  6.  5  and  1  are  6. 

3  and  3  are  6.  6  and  0  are  6. 

7.  6  from  6  leaves  0.  3  from  6  leaves  3. 
5  from  6  leaves  1.  2  from  6  leaves  4. 

4  from  6  leaves  2.  1  from  6  leaves  5. 

8.  A  boy  had  6  marbles  and  lost  3  ;  how  many  mar- 
bles had  he  left  ? 

9.  Six  marbles  less  4  marbles  are  how  many  marbles  ? 

10.  Mary  had  4  cents   and   Henry  gave  her  2  cents 
more.     How  many  cents  had  she  then  ? 

11.  Two  cents  and  4  cents  are  how  many  cents  ? 

12.  How  many  balls  put  with  2  balls  will  make  6  balls  ? 
How  many  with  4  ?     How  many  with  3  ? 

13.  How  many  balls  taken  from  6  balls  will  leave  3 
balls  ?     Will  leave  2  balls  ?     Will  leave  5  balls  ? 

How  many  are 


14.  2  boys  and  4  boys  ? 

15.  3  books  and  3  books  ? 

16.  5  pins  and  1  pin  ? 


17.  6  men  less  2  men  ? 

18.  >5  caps  less  3  caps  ? 
./#.  6  pinks  less  5  pinks  ? 


20  FIRST     BOOK 


LESSON    X. 

1.  Four  trees  and  3  trees  are  how  many  trees  ? 

2.  If  3  trees  be  cut  down,  how  many  will  be  left  ? 

3.  How  many  apples  on  the  tree  ?     3  apples  and  2 
apples  and  2  apples  are  how  many  apples  ? 

4-  If  3  apples  fall  from  the  tree,  how  many  are  left  ? 
If  2  more  fall,  how  rminy  are  left  ? 

5.  Three  girls  and  how  many  more  make  seven  girls  ? 

6.  Seven  bunches  of  grain  are  how  many  more  than 
5  bunches  ?    Than  3  bunches  ?    Than  2  bunches  ? 

7.  How  many  girls  are  shown  in  the  picture  ?     If  1 
girl  leave,  how  many  will  remain  ?    If  3  leave  ?     If  4 
leave  ?    If  2  leave  ?     If  6  leave  ? 

8.  Make  3  lines  on  your  slate.    3  more.        /  /  /  /  /  / 

9.  How  many  more  will  make  seven  ? 

10.  How  many  3?s  in  seven  and  how  many  over  ? 

11.  Write  the  word  seven  on  your  slate.  &even. 

12.  Make  the  figure  that  stands  for  seven.        7. 

13.  Count  seven.     Count  from  seven  back  to  one. 

14.  How  many  are  seven  and  one  more  ?         Eight* 


IK     ARITHMETIC.  21 

LESSON    XL 

1.  How  many  ones  in  seven  ?  1 1 1 1 1 1 1 

2.  How  many  2's,  and  how  many  over  ? 

3.  How  many  3's,  and  how  many  over  ? 

4.  Seven  girls  are  how  many  more  than  2  girls  ?  Than 
5  girls  ?     Than  1  girl  ?     Than  3  girls  ?     Than  4  girls  ? 

5.  Three  and  how  many  make  7  ?    4  and  how  many  ? 
2  and  how  many  ?     5  and  how  many  ? 

6.  Kepeat  this  table. 

1  and  6  are  7.  4  and  3  are  7. 

2  and  5  are  7.  5  and  2  are  7. 

3  and  4  are  7.  6  and  1  are  7. 

7.  7  from  7  leaves  0.  3  from  7  leaves  4. 
6  from  7  -leaves  1.            2  from  7  leaves  5. 
5  from  7  leaves  2.            1  from  7  leaves  6. 

4  from  7  leaves  3.  0  from  7  leaves  7. 

£.  James  had  7  cents,  and  gave  5  cents  for  a  pencil. 
How  many  cents  had  he  left  ? 

9.  George  gave  4  peaches  to  his  brother  and  3  to  his 
sister.  How  many  did  he  give  to  both  ? 

10.  How  many  books  put  with  2  books  will  make  7 
books  ?     How  many  books  are  3  books  and  4  books  ? 

11.  How  many  yards  of  ribbon  cut  from  7  yards  will 
leave  5  yards  ?    Will  leave  1  yard  ?    Will  leave  6  yards  ? 

How  many  are 


12.  4  girls  and  3  girls  ? 
18.  2  horses  and  5  horses  ? 
14.  3  boxes  and  4  boxes  ? 


15.  7  trees  less  3  trees  ? 

16.  6  houses  less 4  houses? 

17.  7  figs  less  5  figs  ? 


22 


FIRST     BOOK 


LESSON    XII. 

1.  How  many  sheep  are  shown  in  the  picture  ? 

2.  There  are  4  sheep  in  one  place  and  4  in  another. 
How  many  in  all  ?    4  and  4  are  how  many  ? 

3.  Eight  cars  are  how  many  more  than  7  ?    How  many 
more  than  6  ?    Than  5  ?   Than  4  ?    Than  3  ?    Than  2  ?" 

^.  Make  eight  lines  on  your  slate  by  2's.      II  II II  II 
By  4's.     ////  fill. 

5.  Count  eight  by  2's.     Count  eight  by  4's. 

6.  How  many  2's  in  eight  ?     How  many  4's  ? 

7.  Eight  sheep  less  4  sheep  are  how  many  sheep  ? 

8.  If  2  cars  are  taken  from  eight  cars,  how  many  cars 
are  left  ?     If  5  are  taken  ?    If  6  are  taken  ? 

9.  Four  sheep,  3  sheep,  and  1  sheep  are  how  many 
sheep  ? 

10.  How  many  are  eight  less  6  ?    Eight  less  5  ? 

11.  Write  the  word  eight  on  your  slate. 

12.  Make  the  figure  that  stands  for  eight.        8. 

13.  Count  eight.     Count  from  eight  back  to  one. 

14.  How  many  are  eight  and  one  more.  Nine. 


IK    ARITHMETIC. 


23 


LESSON    XIII. 

1.  How  many  feet  has  a  sheep  ?     How  many  feet 
have  2  sheep  ?     How  many  4's  in  8  ? 

2.  How  many  hands  has  one  boy  ?     How  many  have 
2  boys  ?     3  boys  ?     4  boys  ? 

3.  How  many  boys  must  hold  up  both  hands,  to  show 
8  hands  ?     How  many  2's  in  8  ? 

4.  Eight  are  how  many  more  than  7  ?     Than  5  ? 
Than  2  ?    Than  6  ?     Than  4  ? 

5.  Eight  less  6  are  how  many  ?  7  less  3  are  how  many  ? 

6.  Eepeat  this  table. 

0  and  8  are  8.  4  and  4  are  8. 

1  and  7  are  8.  5  and  3  are  8. 

2  and  6  are  8.  6  and  2  are  8. 

3  and  5  are  8.  7  and  1  are  8. 


7,   8  from  8  leaves  0. 

7  from  8  leaves  1. 

6  from  8  leaves  2. 

5  from  8  leaves  3. 


4  from  8  leaves  4. 

3  from  8  leaves  5. 

2  from  8  leaves  6. 

1  from  8  leaves  7. 


8.  There  are  2  red  cars,  1  blue  car,  and  5  yellow  cars 
in  a  train.     How  many  in  all  ? 

9.  If  there  are  8  horses  in  a  stable  and  3  be  taken  out, 
how  many  will  be  left  ?    If  5  be  taken  ?    If  1  be  taken  ? 

How  many  are 


10.  4  cows  and  4  cows  ? 

11.  6  hens  and  2  hens  ? 

12.  1  pail  and  7  pails  ? 
IS.  3  words  and  5  words  ? 


14-  8  men  less  1  man  ? 

15.  8  figs  less  5  figs  ? 

16.  8  rings  less  7  rings  ? 

17.  8  dogs  less  3  dogs  ? 


24  FIKSTBOOK 


LESSON    XIV, 

1.  In  the  picture,  how  many  roses  are  shown  ?    How 
many  acorns  ? 

2.  How  many  acorns  on  the  upper  branch  ?    How 
many  on  the  lower  ?    How  many  on  both  branches  ? 

3.  Four  and  5  are  how  many  ?    5  and  4  are  how  many  ? 

4.  Nine  less  5  are  how  many  ?    Less  4  are  how  many  ? 

5.  How  many  3's  in  6  ?     How  many  3's  in  nine  ? 

6.  Nine  are  how  many  more  than  6  ?     6  than  3  ? 

7.  If  5  acorns  drop  from  the  branch,  how  many  are 
left  ?    If  4  more  drop,  how  many  are  left  ? 

8.  If  3  roses  are  picked,  how  many  are  left  ?    If  3 
more  ?    If  3  more  ? 

9.  Make  nine  lines  on  your  slate  by  3's.  ///  ///  /// 

10.  Count  nine  by  ones.     Count  nine  by  3's. 

11.  How  many  4?s  in  nine,  and  how  many  over  ? 

12.  Write  the  word  nine. 

13.  Make  the  figure  for  nine.  9. 
IJ/..  Count  nine.     Count  back  from  nine  to  one. 

15.  How  many  are  nine  and  one  more  ?  Ten. 


IK     ARITHMETIC.  26 

LESSON    XV. 

1.  Make  nine  short  lines. on  your  slate.    ///  ///  /// 

2.  How  many  ones  in  9  ?     How  many  3's  in  9  ? 

3.  If  3  girls  have  3  roses  each,  how  many  have  they  all? 

4.  How  many  must  be  taken  from  9  to  leave  6  ?     To 
leave  4?  To  leave  5?  To  leave  1?  To  leave  7?  To  leave  2? 

5.  Repeat  this  table. 

0  and  9  are  9.  5  and  4  are  9. 

1  and  8  are  9.  6  and  3  are  9. 

2  and  7  are  9.  7  and  2  are  9. 

3  and  6  are  9.  8  and  1  are  9. 

4  and  5  are  9.  9  and  0  are  9. 

6.  9  from  9  leaves  0.  4  from  9  leaves  5. 
8  from  9  leaves  1.  3  from  9  leaves  6. 
7  from  9  leaves  2.  2  from  9  leaves  7. 
6  from  9  leaves  3.  1  from  9  leaves  8. 

5  from  9  leaves  4.  0  from  9  leaves  9. 

7.  There  are  9  leaves  on  two  branches.     If  4  leaves 
are  on  one  of  the  branches,  how  many  are  on  the  other  ? 

8.  A  boy  had  5   peaches   in  one  pocket,   and  4  in 
another.     How  many  had  he  in  both  ? 

9.  If  he  give  away  2  peaches  out  of  each  pocket,  how 
many  will  he  have  left  ? 

How  many  are 


10.  7  tops  and  2  tops  ? 

11.  3  dollars  and  6  dollars  ? 

12.  8  pencils  and  1  pencil  ? 
18.  4  nuts  and  5  nuts  ? 


14.  9  eggs  less  2  eggs  ? 

15.  7  birds  less  5  birds  ? 

16.  8  cats  less  7  cats  ? 

17.  9  mice  less  4  mice  ? 


26 


FIEST    BOOK 


WESSON    XVI. 

1.  Make  5  short  lines  ;  then  5  more  lines.  I  III!  II III 

2.  How  many  ones  make  ten  ?  How  many  5's  make  ten? 

3.  In  the  picture,  how  many  books  are  on  the  upper 
shelf  of  the  bookcase  ?    How  many  on  the  lower  ? 

4.  How  many  cherries  on  the  branch  ? 

5.  If  2  cherries  are  picked,  how  many  remain  ? 

6.  If  2  more  are  picked,  how  many  are  left  ?  If  2  more  ? 

7.  Ten  cherries  less  8  cherries  are  how  many  cherries  ? 

8.  Make  ten  short  lines  by  2's.  //  //  //  //  // 

9.  Count  ten  by  2's.     Count  ten  by  5's. 

10.  How  many  flower-pots  are  on  the  ground  ?     How 
many  are  on  the  stand  ?     How  many  in  all  ? 

11.  Six  pots  and  4  pots  are  how  many  pots  ? 

12.  Ten  pots  less  6  pots  are  how  many  ? 

IS.  Name  each  of  the  numbers  that  can  be  expressed 
by  a  single  figure. 

H.  How  is  the  number  ten  expressed  ? 

15.  Write  the  word,  ten.  Q/en. 

16.  Make  the  figures  to  express  ten.  10. 


ARITHMETIC. 


27 


LESSON    XVII. 

1.  Make  ten  short  lines  on  your  slate.       1 1 1 1 1 1 1 1 1 1 

2.  Ten  are  how  many  ones  ?    How  many  2's  ?     5's  ? 

3.  How  many  4's  in  10,  and  how  many  over  ? 

4.  How  many  must  be  taken  from  10  to  leave  5  ?    To 
leave  4  ?    To  leave  7  ?    To  leave  3  ?     To  leave  2  ? 

5.  John  had  6  marbles  and  bought  4  more.     How 
many  had  he  then  ? 

6.  Mary  had  10  cents  and  gave  3  cents  for  a  pencil. 
How  many  had  she  left  ? 

7.  Eepeat  this  table. 

0  and  10  are  10. 

1  and    9  are  10. 

2  and    8  are  10. 

3  and    7  are  10. 

4  and    6  are  10. 


8. 


10  from  10  leaves  0. 
9  from  10  leaves  1. 
8  from  10  leaves  2. 
7  from  10  leaves  3. 
6  from  10  leaves  4. 


5  and  5  are  10. 

6  and  4  are  10. 

7  and  3  are  10. 

8  and  2  are  10. 

9  and  1  are  10. 

5  from  10  leaves  5. 
4  from  10  leaves  6. 
3  from  10  leaves  7. 
2  from  10  leaves  8. 
1  from  10  leaves  9. 


How  many  are 


9.  5  pins  and  5  pins  ? 

10.  3  trees  and  7  trees  ? 

11.  6  birds  and  4  birds  ? 

12.  2  sheep  and  8  sheep  ? 


13.  9  plums  less  5  plums  ? 

14.  10  pears  less  7  pears  ? 

15.  8  pens  less  5  pens  ? 

16.  10  figs  less  9  figs  ? 


In  all  these  lessons  of  counting  in  series,  the  teacher  should  use 
objects,  or  the  numeral  frame,  until  the  pupil  thoroughly  under- 
stands the  process. 


28 


FIRST     BOOK 


LESSON    XVIII. 

REVIEW. 

1.  In  the  picture,  how  many  blocks  in  each  row  ? 

2.  In  the  first  row,  how  many  blocks  in  the  larger  part? 

3.  Mne  blocks  and  1  more  are  how  many  ?     1  and  9  ? 

4.  Eight  blocks  and  2  more  are  how  many  ?   2  and  8  ? 

5.  Ten  blocks  less  8  blocks  are  how  many  ?  10  less  2  ? 

6.  Ten  blocks  less  3  blocks  are  how  many  ?  10  less  7  ? 

7.  Seven  blocks  and  3  more  are  how  many  ?  3  and  7  ? 

8.  Six  blocks  and  how  many  more  make  10  ?    4  and 
how  many  make  10  ? 

9.  Ten  blocks  less  6  blocks  are  how  many  ?     10  less 
how  many  are  6  ? 

10.  Seven  and  how  many  make  10  ?    3  and  how  manj 
make  10  ? 

11.  Ten  blocks  less  5  blocks  are  how  many  ?    5  from 
10  leave  how  many  ? 

12.  How  many  and  5  make  10  ?    How  many  from  10 
leave  5  ? 

18.  How  many  5's  in  10  ?     How  many  6's  in  10  ? 

Ans.  One  6,  and  4  over. 


ARITHMETIC. 


29 


LESSON    XIX. 

REVIEW. 

1.  Count  by  ones  to  ten. 

2.  Count  by  2's  to  4. 
8.  Count  by  2's  to  6. 

4.  Count  by  3's  to  6. 

5.  Count  by  2's  to  8. 

6.  Count  by  4's  to  8. 

7.  Count  by  3's  to  9. 

8.  Count  by  2's  to  10. 

9.  Count  by  5's  to  10. 

10.  How  many  2's  in  4  ? 

11.  How  many  3's  in  6  ? 

12.  How  many  4's  in  8  ? 
IS.  How  many  3's  in  9  ? 

14.  How  many  5's  in  10? 

15.  Jane  picked  4  pinks  from  one  stem,   3  from  an- 
other, and  2  from  another.     How  many  pinks  had  she  ? 

16.  Oscar  had  10  cents,  and  gave  2  cents  for  a  pen  and 
5  cents  for  a  pencil.     How  many  cents  had  he  left  ? 

17.  If  there  are  6  birds  in  one  cage  and  4  in  another, 
how  many  birds  in  both  cages  ?     How  many  more  in 
one  than  in  the  other  ? 

18.  Willie  caught  five  fishes  ;  how  many  more  must 
he  catch  to  have  8  ? 

19.  There  are  seven  cherries  on  one  part  of  a  twig,  and 
3  on  another.     How  many  cherries  on  both  parts  ? 

20.  If  5  cherries  are  picked,  how  many  will  be  left? 


30 


FIRST     BOOK 


LESSON     XX. 

1.  How  many  balls  on 
the  upper  wire  of  the  Nu- 
meral Frame. 

2.  How  many  are  ten 
balls  and  one  ball  more  ? 

Eleven.      Written  11 

3.  How  many  are  eleven 
balls  and  one  ball  ? 

Twelve.      Written  12 

4.  Twelve  balls  and  one 
more  are 

Thirteen.  Written  13 

5.  Thirteen   balls    and 
one  more  are 

Fourteen.     Written  l'£ 

6.  Fourteen  and  one  more  are 

7.  Fifteen  and  one  more  are 

8.  Sixteen  and  one  more  are 

9.  Seventeen  and  one  more  are 

10.  Eighteen  and  one  more  are 

11.  Nineteen  and  one  more  are 

12.  Count  from  one  to  twenty. 

13.  How  many  units   in   the  n 
number  ten  ?     Write  the  figures  for  ten. 

H.  What  does  the  0,  or  cipher,  denote  ?  Ans.  No  units. 

15.  What  does  the  1  denote  ?  Ans.  One  ten. 

16.  Then,  what  do  the  figures  10  denote  ? 

Ans.  1  ten  and  0  units,  or  ten. 


COUNTING. 


Written 

Fifteen. 

15 

Sixteen. 

16 

Seventeen. 

17 

Eighteen. 

18 

Nineteen. 

19 

Twenty. 

20 

mber   one  ?     In 

the 

ten. 

10 

INAEITHMETIC.  31 

LESSON    XXI. 

1.  When  two  figures  are  written  side  by  side,  what 
does  each  figure  denote  ? 

2.  The  one  on  the  right  denotes  units,  and  the  one 
on  the  left  denotes  tens. 

3.  What  do  the  figures  11  denote? 

Ans.  1  ten  and  1  unit,  or  eleven. 

4.  What  do  the  figures  12  denote  ? 

Ans.  1  ten  and  2  units,  or  twelve. 

5.  What  do  the  figures  15  denote  ? 

Ans.  1  ten  and  5  units,  or  fifteen. 

6.  Write  the  figures  that  stand  for  twenty.  20 

7.  How  many  tens  are  there  in  twenty? 

8.  What  do  the  figures  20  denote  ? 

Ans.  2  tens  and  0  units,  or  tiventy. 

9.  What  then  do  the  figures  21  denote  ? 

Ans.  2  tens  and  1  wmY,  or  twenty-one. 

Written 

./#.  Two  tens  and  two  units  are  Twenty  "two.      22 

11.  Two  tens  and  three  units  are  Twenty-three.  23 

12.  Two  tens  and  four  units  are  Twenty -four.    <£Jj, 

13.  Two  tens  and  five  units  are  Twenty-five.      25 

14.  Two  tens  and  six  units  are  Twenty-six.       26 

15.  Two  tens  and  seven  units  are  Twenty -seven.  27 

16.  Two  tens  and  eight  units  are  Twenty -eight.  28 

17.  Two  tens  and  nine  units  are  Twenty -nine.    29 

18.  Ttiree  tens  and  no  units  are  Thirty.  30 

19.  Count  from  one  to  thirty. 

20.  Write  the  numbers  from  one  to  thirty. 


32  FIKSTBOOK 

LESSON    XXII. 

1.  How  many  units  are  ten  ?  Are  twenty?  Are  thirty  ? 

2.  How  many  tens  are  ten  ?   Are  twenty  ?  Are  thirty  ? 

3.  Count  thirty.     Write  the  figures  that  stand  for 
thirty.  gQ 

4.  Write  the  figures  that  stand  for  thirty-one.     For 
thirty-two.     For  thirty-three. 

5.  What  do  the  figures  34  denote  ? 

Ans.  3  tens  and  4  units,  or  thirty-four. 

6.  Count  from  thirty  to  forty. 

7.  Write  the  numbers  from  thirty  to  forty. 

8.  How  many  units  are  four  tens  ?    How  many  tens 
are  forty  ? 

9.  Make  the  figures  that  stand  for  forty.  ^Q 

10.  Write  the  figures  for  forty-three.     For  forty-four. 

11.  What  do  the  figures  45  denote  ? 

Ans.  4  tens  and  5  units,  OT  forty-five. 

12.  Count  from  forty  to  fifty. 

13.  Write  the  numbers  from  forty  to  fifty. 

14.  How  many  tens  are  fifty  ?     How  many  units  ? 

15.  Write  the  figures  that  stand  for  fifty.  50 

16.  What  do  the  figures  56  denote  ? 

Ans.  5  tens  and  6  units,  or  fifty-six. 

17.  Count  from  fifty  to  sixty. 

18.  Write  the  numbers  from  fifty  to  sixty. 

19.  How  many  tens  are  sixty  ?     How  many  units  ? 

20.  Write  the  figures  that  stand  for  sixty.  QQ 
VI.  What  do  the  figures  67  denote  ? 

Ans.  6  tens  and  7  units,  or  sixty-seven. 


INABITHMETIC.  33 

LESSON*  XXIII. 

1.  Count  from  sixty  to  seventy.     Write  the  numbers 
from  sixty  to  seventy. 

2.  How  many  tens  are  seventy  ?    How  many  units  ? 

3.  Write  the  figures  that  stand  for  seventy.  7$ 

4.  Write  the  figures  for  seventy-five.  For  seventy-seven. 

5.  What  do  the  figures  78  denote  ? 

Ans.  7  tens  and  8  units,  or  seventy -eight. 

6.  Make  the  figures   denoting  seventy-two.      Sixty- 
five.     Seventy-four.     Sixty-three.     Seventy-one. 

7.  Count  from  seventy  to  eighty.     Write  the  num- 
bers from  seventy  to  eighty. 

8.  How  many  tens  are  eighty  ?     How  many  units  ? 

9.  Write  the  figures  that  stand  for  eighty.  80 

10.  For  eighty-one.    For  eighty-two.    For  eighty-three. 

11.  What  do  the  figures  87  denote  ? 

Ans.  8  tens  and  7  units,  or  eiglity-sevm. 

12.  Count  from  eighty  to  ninety.     Write  the  numbers 
from  eighty  to  ninety. 

13.  How  many  tens  are  ninety  ?    How  many  units  ? 

14.  Count  from  ninety  to  one  hundred. 

15.  Write  the  figures  that  stand  for  ninety.  QQ 

16.  What  do  the  figures  99  denote  ? 

Ans.  9  tens  and  9  units,  or  ninety-nine. 

17.  The  greatest  number  that  can  be  expressed  by  two 
figures  is  99. 

18.  Ninety-nine  and  one  more  are  one  hundred* 

Written  100 

19.  What  does  1  mean  with  two  O's  on  the  right  ? 


34  FIRST     BOOK 

©  ©  and  ©  ©  ©      yrji/oNbk  IT)       ©  O  ©  am/  ©  © 

/FSI^BKPHk 
are   ©  ©  ©  ©  ©    xoMMirL     are  ©  ©  ©  ©  © 


2  +  3  are  5      l^P^i       3  +  2  are  5 


PLUS. 

LESSON    XXIV. 

j?.  Make  a  short  horizontal  line  on  your  slate ;  thus,  — . 

2.  Make  a  short  vertical  line  on  your  slate  ;  thus,    |  . 

3.  Make  these  two  lines  to  cross  each  other  ;  thus,  + . 

4.  Because  +  shows  what  is  to  be  done,  it  is  called 
a  Sign. 

5.  This  sign  +  is  named  Plus,  tmtiplus  means  more. 

6.  The  sign  +  is  used  in  place  of  the  word  and;  thus, 
instead  of  writing  2  and  3  are  5,  we  may  write  2  +  3  are  5, 
which  means  2  and  3  more  are  5  ;  and  is  read  2  plus  3 
are  5. 

7.  Eead  the  following : 

5  +  4  are  9.  4  +  4  are  8. 

2  +  5  are  7.  6  +  4  are  10. 

3  +  6  are  9.  7  +  2  are  9. 

8.  How  many  are 

44.39  7  +  2?  3  +  7?  3  +  4? 

2  +  6?  4  +  5?  8  +  1?  4  +  6? 

5  +  3?  5  +  5?  6  +  2?  8  +  2? 

The  foregoing,  with  their  results,  may  be  copied  on 
the  slate ;  thus,  4  +  3  are  7,  etc. 


IK     ARITHMETIC. 


35 


LESSON    XXV. 

i  Counting  two  or  more  numbers  of  the  same  kind 
together,  so  as  to  find  what  number  they  all  equal,  is  called 
adding,  or  Addition. 

2.  The  Plus  Sign,  +  ,  is  the  sign  of  Addition. 

3.  The  sign  -f  shows  that  what  is  written  at  the  right 
of  it  is  to  be  added  to  what  is  written  before  it.     Thus, 
4  +  3  means  that  3  is  to  be  added  to  4. 

4.  The  number  obtained  by  adding  is  called  the  Sum. 
Thus,  9  is  the  sum  of  5  and  4,  or  5  -j-  4. 

5.  Usually,  when  numbers  are  to  be  added,  they  are 
written  in  a  vertical  line,  or  column. 

6.  Add  the   numbers   2,   3,   and  4,  writing  2 
them  as  shown  in  the  margin,  and  draw  a  line              3 
under  the  column.     We  first  find  that  4  and              4 
3  are  7,  and  next,  that  7  and  2  more  are  9,  which     Sum  9 
tte  write  belo^r  the  line  for  the  sum  of  2,  3,  and  4. 

EXERCISES   FOE  THE   SLATE   AND   BLACKBOARD. 

7.  In  like  manner  copy  and  add  the  following  : 
132123,2432 
2433535343 
3214142133 


FIEST     BOOK 


©00)       are        .^fSSim <@ ° and I       are 

of Ooooo  MM       Wlooo     ieoooo 

3  +  2  =  5      'HEW'      2  +  3  =  5 
J^^"- 

EQUALITY. 

LESSON    XXVI. 

1.  Make  two  horizontal  lines  ;  thus,  =. 

2.  Are  these  two  lines  equal  or  unequal  in  length  ? 

3.  Since  these  two  lines  =  are  equal,  we  will  here- 
after use  them  to  mean  equal,  in  place  of  the  word  equal, 
or  of  the  word  are.     Thus, 

4.  Instead  of  writing  3  and  2  are  5,  or  3  +  2  equal  5, 
we  may  write  3  +  2  =  5. 

5.  Because  these  two  lines  mean  e^wa?,  they  are  called 
the  Sign  of  'Equality. 

6.  Copy  and  read  the  following  : 

4  +  2:=  6.        3  +  4  =  7.        5  +  4  =  9.        7  +  3  =  10. 

7.  Write  the  following,  using  figures  and  signs  : 
Three  and  five  equal  eight.          Six  and  three  equal  nine. 
Eight  and  two  equal  ten.  Nine  and  one  equal  ten. 

8.  In  the  following  examples,  =  ?  means  "  equal   how 
many."    In  copying,  find  the  sum  and  write  it  in  the 
place  of  the  question  mark  ( ? ). 

4+2=?  5+5=?  3+3+3=? 

6  +  2=?-          5~+4  =  ?  2  +  2  +  2  =  ? 

5+3=?  8+2=?  2+3+4=? 


IKAKITHMETIC.  37 

LESSON    XXVII. 

1.  If  a  spool  of  thread  costs  6  cents  and  a  yard  of  tape 
4  cents,  how  much  do  both  cost  ? 

2.  Henry  rode  7  miles  and  walked  2  miles.     How  far 
did  he  go  ? 

3.  A  tailor  sold  5  yards  of  cloth  at  one  time  and  5 
yards  at  another.     How  many  yards  did  he  sell  in  all  ? 

4.  Carrie  had  4  roses  and  Nellie  had  3.     How  many 
roses  had  both  ? 

5.  In  a  fruit-dish  are  5  red  apples  and  4  green  ones. 
How  many  apples  in  the  dish  ? 

6.  Two  birds  sit  on  one  limb,  3  on  another,  and  5  on 
another.     How  many  birds  in  all  ? 

7.  A  man  paid  3  dollars  for  a  cord  of  wood  and  6  dol- 
lars for  a  ton  of  coal.     How  much  did  he  pay  for  both  ? 

8.  Susie  bought  a  yard  of  ribbon  for  7  cents  and  some 
buttons  for  3  cents.     How  much  did  she  pay  for  both  ? 

9.  Begin  with  1  and  count  9  by  2?s ;  thus,  one,  three, 
five,  seven,  nine. 

10.  Begin  with  1  and  count  10  by  3's  ;  thus,  one,  four, 
seven,  ten. 

11.  Copy  and  add  the  following  on  your  slate  : 


2 

2 

2 

3 

2 

I 

1 

I 

3 

2 

2 

I 

3 

3 

2 

3 

1 

1 

2 

2 

2 

2 

1 

1 

2 

2 

1 

2 

2 

1 

I 

2 

3 

I 

2 

2 

2 

1 

2 

I 

I 

1 

2 

3 

I 

The  pupil  should  be  required  to  add  as  he  counts,  only  naming 
each  successive  result 


38  FIRST     BOOK 


MINUS. 

LESSON    XXVIII. 

./.  Make  a  short  horizontal  line  on  your  slate  ;  thus,  —  . 

2.  A  line  written  thus  —  ,  between  two  numbers,  is 
used  to  mean  less,  in  place  of  the  word  less.     Thus, 

3.  Instead  of  writing,  2  from  5  leaves  3,  or  5  less  2 
equals  3,  we  may  write  5  —  2  =  3. 

4.  The  sign  —  is  named  Minus,  and  minus  means 
less. 

5.  Eead  the  following  : 

8-2  =  6.  9-5  =  4.  10-4  =  6.  8-6  =  2. 
7  —  3  =  4.  6  —  6  =  0.  7  —  4  =  3.  10  —  3  =  T. 
9  —  4  =  5.  8  —  5  =  3.  9  —  2  =  7.  7  —  7  =  0. 

6.  "Write  the  following,  using  figures  and  signs  : 
Nine  less  two  equals  seven.      Ten  less  five  equals  five. 
Seven  less  two  equals  five.        Eight  less  one  equals  seven. 
Six  less  four  equals  two.  Seven  less  four  equals  three. 

7.  Copy  the  following,  writing  the  result  in  place  of 
the  question  mark  (?). 

8-1  =  ?  5-4  =  ?  5-5  =  ?  10-2  =  ? 
7  —  5  =  ?  10  —  6  =  ?  9  —  6  =  ?  9  —  8  =  ? 
9—3=?  7—2=?  8—7=?  3—3=? 


ARITHMETIC. 


39 


LESSON    XXIX. 

1,  Taking  one  number  from  another  of  the  same  kind 
is  called  subtracting,  or  Subtraction. 

2.  The  Minus  Sign  —  is  the  sign  of  Subtraction. 

8.  The  sign  —  shows  that  what  is  written  at  the  right 
is  to  be  taken  from  what  is  written  before  it;  Thus, 
6  —  4  means  that  4  is  to  be  subtracted  from  6. 

4.  The  number  that  shows  how  many  remain  after 
subtracting  is  called  the  Remainder,  sometimes  the 
Difference.    Thus, 

5  is  the  remainder  after  taking  4  from  9,  or  5  is  the 
difference  between  9  and  4,  written  9  —  4  =  5. 

5.  Find  the  remainder  of 

7  less  5  10  less  4  8-4  7-6 

9  less  2  6  less  6  9  —  6          10  —  2 

6.  In  performing  Subtraction,  the  numbers  when        7 
written  are  usually  arranged  as  in  the  margin,  the        4 
smaller  under  the  greater,  with  a  line  drawn  under-        3 
neath.     We  say  4  from  7  leaves  3,  which  we  write 
below  the  line  for  the  remainder. 

EXERCISES  FOR  THE  SLATE  AHD  BOARD. 

7.  Copy  and  write  the  remainder  in  each  of  the  following: 
56879        10        8        10        79 
34253          75          572 


40  FIRST     BOOK 

LESSON     XXX. 


1.  Here  is  a  picture  of  twelve  stars. 

2.  Count  twelve.     Make  the  figures  for  twelve.     12 
8.  Count  from  12  back  to  1. 

4.  Count  by  2's  to  8.     Count  from  8  back  to  0. 

Ans.  Eight,  six,  four,  two,  naught. 
6.  How  many  are  8  less  2  ?  6  less  2  ?  4  less  2  ?  2  less  2  ? 

6.  Count  by  2's  to  10.     Count  from  10  back  to  0. 

7.  How  many  are  10  less  2  ?     8  less  2  ?     6  less  2  ? 

8.  Count  by  2's  to  12.     Count  from  12  back  to  0. 

9.  Count  by  3's  to  9.     Count  from  9  back  to  0. 

10.  How  many  are  9  less  3  ?     6  less  3  ?     3  less  3  ? 

11.  Count  by  3's  to  12.     Count  from  12  back  to  0. 

12.  How  many  are  12  less  3  ?     9  less  3  ?     6  less  3  ? 
3  less  3  ? 

18.  How  many  3's  in  12  ?     How  many  2's  ? 

14.  If  there  are  12  sheep  in  a  yard  and  3  jump  out, 
how  many  sheep  are  left  ?     12  —  3  =  ? 

15.  If  3  more  jump  out,  how  many  are  left  ?  9 — 3=  ? 

16.  If  3  more  jump  out,  how  many  are  left  ?  6 — 3=  ? 

17.  If  6  more  jump  out,  how  many  are  left  ?  3— 3=  ? 

18.  Write  on  your  slates  the  following,  using  the  proper 
igns  and  the  correct  number  in  the  place  of  the  (  ?). 

3  and  3  and  3  are  9.  9  less  5  equal  4. 

2  and  3  and  3  =  ?  10  less  7  =  ? 

3  and  1  and  3  are  7.  5  from  8  leaves  ? 
2  and  3  and  2  =  ?              6  from  9  leaves  3. 


IK    ARITHMETIC.  41 

LESSON    XXXI. 

1.  Begin  with  1  and  count  by  2's  to  11. 

Ans.   One,  three,  five,  seven,  nine,  eleven. 

2.  Begin  with  1  and  count  by  2's  to  13. 

3.  Begin  with  1  and  count  by  3's  to  10.     By  3's  from 

1  to  13.     From  2  to  14. 

4*  Begin  with  2  and  count  by  3's  to  11.     By  3's  from 

2  to  14. 

5.  Begin  with  1  and  count  by  4's  to  9.     By  4's  from 

2  to  10. 

6.  Begin  with  2  and  count  by  4's  to  14.     By  4's  from 

3  to  15. 

EXERCISES  FOR  THE  SLATE  AKD  BOARD. 

7.  In  like  manner  jcount  and  find  the  sum  in  each  of 
the  following  : 


3 

3 

3 

2 

4 

4 

1 

2 

3 

0 

3 

4 

3 

2 

4 

3 

2 

3 

2 

3 

3 

3 

3 

2 

4 

2 

3 

4 

1 

4 

3 

1 

2 

2 

4 

1 

3 

1 

4 

4 

8.  Find  the  remainder  to  each  of  the  following  : 

7        9        6        8        7        9       10      11        5       12 
3463634728 

9.  Find  and  write  the  result  in  each  of  the  following  : 

2  +  2  +  2  +  2  +  2=?  9  —  1=? 

=?  3  +  3  +  3  +  2  +  1=?          10-7=? 

2  +  4  +  3  +  1=?  1  +  2  +  3  +  4  +  0=?  5-5=? 

1  +  3  +  0  +  4=?  3  +  1  +  4  +  2  +  1=?  9— 6="? 


42  FIRST     BOOK 

LESSON    XXXII. 

1.  Four  and  four  are  how  many  ? 

2.  Eight  and  4  are  how  many  ?     12  and  4  ? 
8.  Count  12  by  4's.     How  many  4's  in  12  ? 

4.  Four  from  12  leaves  how  many  ?    4  from  8  ? 

5.  Twelve  are  how  many  more  than  8  ?  More  than  4  ? 

6.  Four  and  how  many  make  8  ?     8  are  how  many 
less  than  12  ? 

7.  Begin  with  1  and  count  by  4's  to  17. 

Am.  One,  five,  nine,  thirteen,  seventeen. 

8.  Begin  with  2  and  count  by  4's  to  18. 

9.  Begin  with  3  and  count  by  4's  to  19. 

10.  Begin  with  0  and  count  by  4's  to  20. 

11.  How  many  are  20  less  4  ?     16  less  4  ?     12  less  4  ? 

When  the  Sum  of  two  or  more  numbers,  or  the  Differ- 
ence of  two  numbers,  is  named  instantly,  it  is  called 
addition,  or  subtraction,  at  sight.  Thus,  in  the  example 
4  +  3,  say  1,  instead  of,  4  and  3  are  7. 

Addition  at  Sight. 

4421335444 
4345343687 

Subtraction  at  Sight. 

4865787698 
^432354553 

At  recitation  the  teacher  may  write  similar  exercises  on  the 
board,  and  point  from  one  set  of  numbers  to  another,  as  rapidly  as 
the  class  can  name  the  results. 


IH     ARITHMETIC.  43 

LESSON    XXXIII. 

1.  Four  are  how  many  less  than  9  ?    9  are  how  many 
more  than  5  ? 

2.  How  many  are  12  less  7  ?    12  less  5  are  how  many  ? 
$.  Ira  gave  5  cents  for  a  pencil  and  4  cents  for  a  top. 

How  much  did  both  cost  ? 

4.  John  has  6  books  and  Jane  has  5  books.     How 
many  books  have  both  ? 

5.  James  gave  7  cents  for  a  writing-book  and  had  5 
cents  left.     How  many  cents  had  he  at  first  ? 

£.8  +  4=?  3  +  5  +  2:=?  io~5  =  ? 

7  +  5  =  ?  4  +  5  +  2  —  ?  11  —  3  =  ? 

8^+3  =  ?  6  +  4  +  4=?  12  —  4=? 

7.  Asa  is  9  years  old ;  how  old  will  he  be  4  years  hence  ? 

8.  Martha  is  12  years  old ;  her  sister  is  4  years  younger. 
How  old  is  her  sister  ? 

9.  There  were  11  geese  and  4  ducks  swimming  on  the 
pond.     How  many  are  there  of  both  ?    How  many  more 
geese  than  ducks  ? 

10.  A  beggar  met  two  boys  ;  one  gave  him  5  cents,  the 
other  gave  him  4.     How  many  cents  did  both  give  him  ? 

EXERCISES  FOE  SLATE  AKD  BOARD. 
11    Copy  and  add  : 


4 

4 

4 

4 

4 

4 

3 

5 

2 

1 

4 

4 

-   4 

4 

3 

4 

4 

2 

4 

2 

4 

4 

4 

4 

5 

3 

2 

4 

3 

4 

4 

3 

2 

1 

3 

2 

1 

2 

4 

5 

44  FIESTBOOK 

LESSON    XXXIV. 

1.  How  many  are  5  cents  and  5  cents  ? 

2.  How  many  are  10  cents  and  5  cents  more  ? 

3.  How  many  are  15  cents  and  5  cents  more  ? 

4.  Count  10  by  5's.    Count  15  by  5's.    Count  20  by  5's. 

5.  How  many  5's  in  10  ?    How  many  5's  in  15  ?    How 
many  5's  in  20  ? 

6.  Twenty  less  5  are  how  many  ?   15  less  5  ?   10  less  5  ? 

7.  How  many  are 

5  +  5  ?  2  +  5  +  5?  20-5?  14-5? 
4  +  5  ?  3  +  5  +  5  ?  15  —  5?  13  —  5? 
3  +  5?  4  +  5  _}_  5  ?  10-5?  12-5? 

2  +  5?          5  +  5  +  5?  5  —  5?          17  —  5? 

8.  Count  by  5's  from  15  back  to  0.    From  20  back  to  0. 

9.  Count  by  5's  to  25.     From  25  back  to  0. 

10.  Twenty-five  less  5  are  how  many  ?     20  less  5  ? 
15  less  5  ?    10  less  5  ?    5  less  5  ? 

11.  Count  by  5's  from  1  to  16.    From  2  to  17.    From 
3  to  18.    From  4  to  19. 

EXERCISES  FOE  THE  SLATE  AND  BOARD. 

12.  Copy,  count,  and  write  the  sum  of  the  following  : 


5 

5 

5 

5 

5 

1 

2 

3 

2 

4 

5 

5 

5 

5 

5 

5 

5 

2 

5 

1 

5 

5 

5 

5 

5 

5 

5 

1 

3 

2 

5 

5 

5 

5 

5 

5 

5 

4 

1 

3 

5 

1 

2 

3 

4 

5 

5 

5 

4 

5 

Vary  this  exercise  in  a  thorough  drill,  making  all  combinations 
with  figures  not  greater  than  5,  and  making  a  sum  not  to  exceed  25. 


IN     ARITHMETIC.  45 

LESSON    XXXV. 

1.  How  many  5's  in  10  ?    How  many  2's  ? 

2.  How  many  5's  in  15  ?    How  many  3's  ? 

3.  How  many  5's  in  20  ?    How  many  4's  ? 

^.  Count  25  by  2's,  beginning  with  1.  Count  25  by  5's. 

5.  Begin  with  4  and  count  by  3's  to  25. 

6.  How  many  are  8  boys  and  4  boys  ?    12  boys  less 

4  boys  ?    13  boys  less  5  boys  ? 

7.  How  many  are  6  girls  and  5  girls  ?    11  girls  less 

5  girls  ?    12  girls  and  5  girls  ? 

8.  How  many  are  15  marbles  less  5  marbles  ?  15 — 5 =? 

9.  Fourteen  books  less  5  books  are  how  many  books  ? 

10.  Asa  had  12  marbles  and  lost  all  but  5  ;  how  many 
did  he  lose  ? 

EXEKCISES   FOE  THE   SLATE   AND   BOARD. 

11.  Write  the  proper  numbers  in  place  of  (?)  : 

5  +  ?=6  8  +  5=?  10+?=15  8+?=10 

?— 2=5          10_5_?  12—?=  2          10—  ?=  8 


Addition. 
553?         ?95?          ?        2 

4_?_I_1_1_1^1^_?.-?. 
?         ?       10      11        9       14        ?       15       12        ? 

£tt&£me£ion. 

9      12      10         ??       14        8         ?      15        9 

J!JLJ^-1-1_L-_L_Z_^_£ 
57P461001?? 


46  FIRST     BOOK 


3  fours  are  12       ^fc^fe^       4  three*  &re  12 
@»    ®®    ?°        IjWSi          o   o   S   e 

©  ©  ©  ®  ©  o     /VA^E'^Myvk 

3  times  4  are  12    ^B|fiB^    4  *MH*$  3  are  12 

MULTIPLICATION. 

LESSON    XXXVI. 

1.  If  you  pay  4  cents  for  1  lemon,  how  many  times 
4  cents  must  you  pay  for  3  lemons  ?  4  +  4  +  4=?  How 
many  are  three  4's  ? 

2.  Instead  of  writing  4  +  4  +  4  =  1 2,  we  may  write 
3  times  4  are  12. 

3.  If  1  orange  cost  3  cents,  how  many  times  3  cents 
must  you  give  for  4  oranges  ?    3  +  3  +  3+3  =  ?    How 
many  are  four  3's  ? 

4.  Instead  of  writing  3  +  3  +  3  +  3  =  12,  we  may 
write  4  times  3  are  12. 

5.  Make  a  short  line  on  your  slate,  inclined ;  thus,  / 

6.  Make  another  short  line,  inclined;  thus,   \ 

7.  Make  these  two  lines  cross  each  other  ;  thus,  x 

8.  This  sign,  x ,  is  used  in  place  of  the  word  times  ; 
thus,  instead  of  writing  3  times  4  are  12,  or  4  times  3 
are  12,  we  may  write  4  x  3  are  12,  or  3  x  4  =  12. 

9.  Eead  the  following  : 

2  x  3  are  6.         4  x  3  are  12.         4x2=    8. 

3  x  3  are  9.         3x4  are  12.         5x2  =  10. 
1  X  4  are  4.         0  x  3  are    0.         5x3  =  15. 


ARITHMETIC. 


47 


Ml         TICATIOTV 


LESSON    XXXVII. 

1.  If  you  take  4  peaches  3  times  from  a  fruit  dish, 
how  many  peaches  will  you  take  in  all  ? 

2.  How  many  peaches  are  3  times  4  peaches  ? 

8.  When  4  is  taken  as  many  times  as  there  are  ones 
or  units  in  3,  how  many  times  is  it  taken  ? 

4.  Taking  one  of  two  numbers  as  many  times  as  there 
are  ones  or  units  in  another  is  called  Multiplication. 

5.  The  x  is  called  the  Sign  of  Multiplication* 
It  is  read  times,  or  multiplied  by  ;  thus,  3  x  2  is  read 
3  multiplied  by  %,  or  2  times  3 ;  4  x  3  is  read  4  multiplied 
ly  3,  or  3  times  4. 

6.  The  number  obtained  by  multiplying  one  number 
by  another  is  called  the  Product. 

MULTIPLICATION  TABLE. 

2x0=  0  3x0=  0 

2x1=  2  3x1=  3 

2x2=  4  3x2=  6 

2x3=  6  3x3=  9 

2x4=  8  3x4=12 

2x5=10  3x5  =  15 

The  above  tables  should  be  thoroughly  memorized  and  repeated 
both  in  the  direct  and  reverse  order  ;  thus,  2  times  3  are  6,  3  times 
2  are  6,  2  times  4  are  8,  4  times  2  are  8,  etc. 


4x0=  0 

5x0=  0 

4x1=  4 

5x1=  5 

4x2=  8 

5x2=10 

4x3=12 

5x3=15 

4x4=16 

5x4=20 

4x5=20 

5x5=25 

FIBST     BOOK 


LESSON    XXXVIII. 


1.  How  many  oranges  are  5  times  3  oranges  ? 

2.  There  are  two  ways  of  solving 
this  example. 

FIRST. — Write  the  figure  3  five 
times  in  a  column,  and  draw  a  short 
line  under  it.  Then  count,  or  add, 
thus  :  3,  6,  9,  12,  15,  and  write  the 
result  below  the  line. 

SECOND. — Write  the  figure  3  but 
once,  and  write  the  figure  5  under  it, 
to  show  hoiv  many  times  3  is  to  be 
taken,  and  draw  a  short  line.     Then  By  Multiplication* 
say  5  times  3  are  15,  and  write  the  3 

result  below  the  line.    The  result  is  _5 

15  in  both  cases,  but  in  the  first  case  ^5  Product. 

it  is  obtained  by  addition  and  is  called 
the  Sum  ;  in  the  second  case,  it  is  obtained  by  multipli- 
cation and  is  called  the  Product.     Hence, 

3.  Multiplication  is  also  a  short  method  of  adding  equal 
numbers. 

5x2=i?  5x5=?  3x5=?  4x5=? 

5x3=?  3x4=?  3x3=?  4x4=P 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 
Find  the  result  by  Addition  and  by  Multiplication 


FIRST. 

By  Addition. 
3 
3 
3 
3 
J3 

15  Sum. 
SECOND. 


'4'  Of  2  times  5  cents. 

5.  Of  4  times  3  figs. 

6.  Of  3  times  5  marbles. 


7.  Of  5  times  4  hats. 

8.  Of  5  times  2  boys. 

9.  Of  4  times  5  peaches. 


IN     ARITHMETIC.  49 

LESSON    XXXIX. 

1.  How  many  peaches  are  there  on  3  plates,  if  there 
are  5  peaches  on  each  plate  ? 

SOLUTION. — Since  there  are  5  peaches  on  one  plate,  on  3  plates 
there  are  3  times  5  peaches,  which  are  15  peaches.  Hence,  there 
are  15  peaches  on  3  plates. 

2.  If  a  yard  of  ribbon  cost  4  cents,  how  much  will 
3  yards  cost  ? 

3.  If  1  orange  cost  5  cents,  what  will  2  oranges  cost  ? 

4.  How  much  will  4  pencils  cost,  if  1  pencil  cost  5 
cents  ? 

5.  How  many  eggs  in  3  nests,  if  there  are  3  eggs  in 
each  nest  ? 

6.  How  many  marbles  have  4  boys,  if  each  boy  has 
5  marbles  ? 

7.  How  many  fishes  did  3  boys  catch,  if  each  boy 
caught  5  fishes  ? 

8.  Mary  gave  5  cents  a  yard  for  5  yards  of  ribbon. 
How  many  cents  did  she  give  for  the  whole  ? 

9.  Which  is  greater,  4  times  5,  or  5  times  4  ? 

10.  How  much  greater  is  4  times  3  than  2  times  5  ? 

11.  What  is  the  difference  in  the  cost  of  3  oranges  at 
5  cents  a  piece,  and  5  lemons  at  3  cents  a  piece  ? 

EXEKCISES   FOR  THE   SLATE   A^D   BOARD. 

Multiplication  at  Sight. 

5434455355 
2354534305 


50  PIKST     BOOK 

©      O      ©  ©      ©      © 

o  o  o    Jii|s  SP||>    ©  ©  © 

4  in  12,  3  times,    l^gti^^  1  third  of  12  is  4 

±£  •"•  *  ••  &  ^'^/^  3 

DIVISION. 

LESSON    XL. 

1.  I  had  12  marbles  and  gave  4  to  James  ;  how  many 
had  I  left  ? 

2.  I  gave  4  more  to  Louis ;  then,  how  many  had  I  left  ? 

3.  I  gave  4  more  to  Asa  ;  then,  how  many  had  I  left  ? 

4.  How  many  times  4  marbles  did  I  give  away  ? 

5.  How  many  are  12  less  4  ?    8  less  4  ?    4  less  4  ? 

£.  How  many  times  can  4  marbles  be  taken  from  12 
marbles  ?     How  many  4's  in  12  ? 

7.  Instead  of  saying  that  4  can  be  taken  from  12, 
3  times,  or  that  there  are  3  fours  in  12,  say,  4  is  contained 
in  12,  3  times. 

8.  Make  a  short  horizontal  line  on  your  slate  ;  thus,  — 

9.  Make  two  dots,  one  above,  and  one  below  the  line  ; 
thus,  -7- 

10.  This  sign,    -r-,   is  used  in    place  of    the    words 
divided  by ;   thus,  instead  of  writing  12  divided  ~by  4, 
write  12  ~  4. 

11.  Express  by  figures  and  the  proper  signs:   Two  is 
contained  in  twelve,  six  times.    Four  is  contained  in  twen- 
ty, five  times.    Five  is  contained  in  twenty-five,  five  times. 


ARITHMETIC. 


51 


(DIVISION 


LESSON    XLI. 

1.  How  many  oranges,  at  five  cents  each,  can  you  buy 
for  15  cents  ? 

2.  How  many  times  can  5  cents  be  taken  from  15  cents  ? 

3.  How  many  times  5  cents  in  15  cents  ?    5  is  con- 
tained in  15  how  many  times  ?     15  -h  5  =  ? 

4.  Finding  how  many  times  one  number  is  contained 
in  another  is  called  Division. 

5.  The  sign,  -=-,  is  called  the  Sign  of  Division. 
It  is  read,  divided  by  ;  thus,  15-1-5  is  read,  15  divided  by  5. 

6.  The  number  obtained  by  -dividing  one  number  by 
another  is  called  the  Quotient. 

DIVISION  TABLE. 

0_2=0  0-3=0 

2_2  =  1  3—3=1 

4—2=2  6-3=2 

6—2=3  9—3=3 

8—2=4  12—3=4 

10—2=5  15—3=5 

7.  Write  the  following,  putting  the  quotient  after  the 
sign  =  in  the  place  of  (?). 

8-^2=?  15-r-3=?  20-^4=?  25-5-5=? 

10-5-2=?  10-5-5=?  5—5=  ?  20-r-5=? 


0- 

-4=0 

0- 

-5=0 

4- 

-4=1 

5- 

-5=1 

8- 

-4=2 

10- 

-5=2 

12- 

-4=3 

15- 

-5=3 

16- 

-4=4 

20- 

-5=4 

20- 

-4=5 

25- 

-5=5 

FIRST     BOOK 


LESSON    XLII. 

1.  Among  how  many  boys  can  15  cents  be  divided  and 
each  boy  receive  5  cents  ? 

2.  There  are  two  ways  of  solving  this  example  : 
FIRST. — Taking  5   cents   from   15 

cents,  10  cents  are  left ;  again,  taking 
5  cents  from  10  cents,  5  cents  are  left ; 
again,  taking  5  cents  from  5  cents,  no 
cents  are  left.  Since  5  cents  have 
been  subtracted  or  taken  from  15  cents 
3  times,  I  gave  the  15  cents  to  3  boys. 
SECOND. — Since  we  wish  to  find 
how  many  times  5  cents  are  contained 
in  15  cents,  write  the  expression  thus, 
15-r-5=:3,  and  read  it,  15  divided  ~by  5 
equals  3.  Or,  write  15,  and  on  the 
left  write  5,  with  a  short  curved  line 
between  them,  and  a  short  line  under 
the  15.  Then  say,  5  is  contained  in 
15,  3  times,  and  write  the  result  below  the  line. 

3.  The  result  is  3  in  both  cases,  but  in  the  first  case  it 
is  obtained  by  Subtraction,  in  the  second  case  by  Dim- 
sion.     Hence,  Division  is  also  a  short  method  of  per- 
forming several  subtractions  of  the  same  number. 

4.  Find  the  result,both  by  Subtraction  and  by  Division 
of  each  of  the  following  : 

How  many 

5.  3's  in  12  ?          7.  4's  in  20  ?  9.  5's  in  20  ? 

6.  4's  in  16  ?          8.  3's  in  15  ?         10.  5's  in  25  ? 


FIRST. 

By  Subtraction. 
1 5  cents. 
_J> 

1 0  cents. 
J> 

5  cents. 
5 

0  cents. 

SECOND. 
By  Division. 
5)15 
3 


IK     ARITHMETIC.'  53 

LESSON    XLIII. 

1.  How  many  times  2  cents  in  10  cents  ?    In  12  cents  ? 

2.  How  many  times  3  days  in  12  days  ?     In  15  days  ? 
8.  How  many  times  4  plums  in  12  plums?  In  16  plums? 

4.  How  many  times  5  hours  in  15  hours  ?    In  20  hours  ? 

5.  At  5  cents  each,  how  many  toys  can  be  bought 
for  20  cents  ? 

SOLUTION. — As  many  toys  as  5  cents  are  contained  times  in  20 
cents,  which  are  4  times.    Hence  4  toys  can  be  bought  for  20  cents. 

6.  At  2  cents  each,  how  many  pears  can  be  bought  for 
10  cents  ? 

7.  How  many  quarts  of  milk  at  4  cents  a  quart,  can 
be  bought  for  16  cents  ? 

8.  If  1  lemon  cost  3  cents,  how  many  lemons  can  be 
bought  for  15  cents  ? 

9.  To  how  many  boys  can  you  give  12  apples,  if  you 
give  them  4  apples  apiece  ? 

10.  How  many  hats  can  be  bought  for  25  dollars,  at 
5  dollars  apiece  ? 

11.  Ella  paid  20  cents  for  some  ribbon,  at  5  cents  a 
yard.     How  many  yards  did  she  buy  ? 

12.  Clarence  gave  16  cents  for  some  tops,  at  4  cents  a 
piece.    How  many  tops  did  he  buy  ? 

Division  at  Sight. 

8-1-2=:?  8-5-4=?  15-f-5=?  15-^-3=? 

6-^3=?  10-r-5=?  10-4-2=?  16-4-4=? 

4)_20        5)^5        4)_16        5)J20        3)15        2)_12 


54  FIRST     BOOK 

LESSON    XLIV. 

EQUAL  PARTS  OF  NUMBERS. 

1.  If  6  oranges  are  divided  equally  between  2  girls, 
into  how  many  equal  parts  are  the  oranges  divided? 

2.  When  a  number  is  divided  into  2  equal  parts,  whal 
is  one  of  the  parts  called  ?      One-half  of  the  number. 

8.  How  many  oranges  are  one-half  of  6  oranges  ? 


6  ~-  2  =  3,  or    one-half  of  6  is  3. 

4.  How  many  boys  are  one-half  of  8  boys  ? 

5.  How  many  peaches  are  one-half  of  10  peaches  ? 

6.  If  you  put  10  bushels  of  apples  into  2  boxes,  what 
part  of  the  whole  do  you  put  into  1  box  ? 

7.  Instead  of  finding  how  many  times  one  number  is 
contained  in  another  of  the  same  kind,  it  is  sometimes 
required  fco  divide  a  number  into  equal  parts.     The  opera- 
tion in  both  cases  is  the  same,  but  the  reasoning  is  some- 
what different.     Thus, 

8.  At  3  cents  each,  how  many  pears  can  be  bought 
for  6  cents  ? 

SOLUTION. — As  many  pears  as  3  cents  are  contained  times  in  6 
cents,  which  are  2  times.  Hence  2  pears  can  be  bought  for  6  cents. 
6-5-3  =  2. 

9.  Again,  if  2  pears  cost  6  cents,  what  will  1  pear  cost  ? 

SOLUTION. — If  2  pears  cost  6  cents,  1  pear  will  cost  one-half  of 
6  cents,  which  is  3  cents.  6-^2  =  3. 


Itf     ARITHMETIC.  55 

10.  If  12  cherries  are  divided  equally  among  3  boys, 
into  how  many  equal  parts  are  they  divided  ? 

11.  When  a  number  is  divided  into  3  equal  parts,  what 
is  one  of  the  parts  called  ?     One-third  of  the  number. 

12.  How  many  cherries  are  one-third  of  12  cherries  ? 


12  -r-  3  =  4,       or    one-third  of  12  is  4. 

./#.  How  many  cents  are  one-third  of  9  cents  ? 

H.  How  many  marbles  are  one- third  of  15  marbles  ? 

15.  If  12  pinks  grow  upon  4  stems,  each  containing  an 
equal  number,  how  many  grow  upon  each  stem  ? 

16.  When  a  number  is  divided  into  4  equal  parts,  what 
is  one  of  the  parts  called  ?    One-fourth  of  the  number. 

17.  How  many  pinks  are  one-fourth  of  12  pinks  ? 


12  —  4  =  3,  or    one-fourth  of  12  is  3. 

18.  How  many  dollars  are  one-fourth  of  8  dollars  ? 

19.  What  is  one-fourth  of  12  ?     Of  16  ?     Of  20  ? 

20.  When  a  number  is  divided  into  5  equal  parts,  what 
is  one  of  the  parts  called  ?       One-  fifth  of  the  number. 

21.  How  many  balls  are  one-fifth  of  20  balls  ? 

®®      @^       ®j@      QUO  a® 


20  -T-  5  =  4,        or    one-fifth  of  20. 
#.  How  many  cents  are  one-fifth  of  15  cents  ? 


56  FIRST     BOOK 

LESSON    XLV. 

1.  One-half  is  written  thus,  £.     £  of    6  is    6—2—3. 

2.  One-third  is  written          %.     %  of    6  is    6—3=2. 
8.   One-fourth  is  written        }.     £  of    8  is    8—4=2. 

4.  One-fifth  is  written  -£.     •£  of  15  is  15—5=3. 

5.  How  many  halves  in  any  thing  ?     How  many  thirds 
in  any  thing?     How  many  fourths  in  any  thing?     How 
many  fifths  in  any  thing  ? 

6.  What  is  \  of  4 books?  \  of  10  miles?  £  of  8  houses? 

7.  What  is  £  of  6  sheep  ?  J.  of  9  weeks  ?  £  of  12  dollars? 

8.  What  is  £  of  4  men  ?  J  of  1 6  pounds  ?  ±  of  20  chairs  ? 

9.  What  is  4  of  10  barrels  ?  £  of  15  trees  ?  -J-  of  25  dollars  ? 
.70.  How  do  you  obtain  one-half  of  a  number  ?     One- 
third  of  a  number  ?     One-fourth  of  a  number  ?     One- 
fifth  of  a  number  ? 

1.7.  If  20  marbles  be   divided  equally  among  4  boys, 
how  many  marbles  will  each  boy  receive  ? 

SOLUTION. — Since  20  marbles  are  divided  equally  among  4  boys, 
one  boy  will  receive  one-fourth  of  20  marbles,  or  5  marbles. 

12.  If  3  books  cost  15  cents,  what  is  the  cost  of  1  book  ? 

13.  Write  on  your  slates,  in  a  column,  all  the  num- 
bers from  10  to  20.     Eead  them. 

14.  Write  the  numbers  from  20  to  30,  and  read  them. 
I/).  Write  the  numbers  from  30  to  40,  and  read  them. 

16.  In  a  similar  manner  write  and  read  the  numbers 
from  40  to  50.     From  50  to  60.     From  60  to  70.     From 
70  to  80.     From  80  to  90.     From  90  to  100. 

17.  How  many  figures  are  required  in  writing  each 
number  from  9  to  99  ? 


IK     ARITHMETIC.  5? 

LESSON    XLV1. 

1.  How  many  are  5  and  1  ?    3  and  3  ?    4  and  2  ? 

2.  How  many  are  6  and  6  more  ?     12  and  6  more  ? 

3.  How  many  are  18  and  6  ?     24  and  6  ? 

4.  How  many  are  three  6's  ?     Four  6's  ?     Five  6's  ? 

5.  Count  by  6's  to  12.     To  18.     To  24.     To  30. 

6.  How  many  are  30  less  6  ?    24  less  6  ?     18  less  6  ? 
12  less  6  ?     6  less  6  ? 

7.  Begin  with  1  and  count  .by  6's  to  13.  To  19.  To  25. 

8.  Begin  with  2  and  count  by  6's  to  20.  To  26.  To  32. 

9.  How  many  are 

6  +  6  +  6?  4  +  6  +  6?  2  +  6  +  6? 

5  +  6  +  6?  3  +  6  +  6?  1  +  6  +  6? 

10.  How  many  are 

18  —  6?          15-6?  9-6?          8-6? 

.12  —  6?          11  —  6?          13  —  6?          6  —  6? 

11.  How  many  are 

3  times  6  ?        4  times  6  ?        6x5?        3x6? 
5  times  6  ?        2  times  6  ?        1x6?        6x6? 

12.  How  many 

6's  in  18  ?  6's  in  30  ?  4's  in  16  ? 

6's  in  24  ?  5's  in  20  ?  5's  in  25  ? 

EXERCISES  FOR  THE  SLATE  AKD  BOARD. 
IS.  Copy  and  add  or  count  the  following  ; 
6666666542 
6666665664 
6666664356 
6543212435 


58  FIRST    BOOK 

LESSON    XLVII. 

1.  If  18  figs  are  equally  divided  among  6  boys,  into 
how  many  equal  parts  are  the  figs  divided  ? 

2.  When  a  number  is  divided  into  6  equal  parts,  what 
is  one  of  the  parts  called  ?     One-sixth  of  the  number. 

8.  How  many  figs  are  one-sixth  of  24  figs  ? 


24  -f-  6  =  4,        or      one-sixth  of  24  is  4. 

4.  If  24  plants  are  set  in  6  equal  rows,  what  part  of  24 
plants  is  set  in  1  row  ?     How  many  plants  ? 

5.  One-sixth  is  written  thus,  £.       |  of  24  is  24 -s- 6 =4. 

TABLES. 

ADDITION.  SUBTRACTION.  MULTIPLICATION.  DIVISION. 

0  +  6=  6             6—6=0  6x0=  0  0—6=0 

1  +  6=  7             7-6=1  6x1=  6  6-6=1 

2  +  6=  8             8—6=2  6x2  =  12  12—6=2 

3  +  6=  9             9—6=3  6x3  =  18  18—6=3 

4  +  6  =  10  10-6=4  6x4=24  24—6=4 

5  +  6  =  11  11—6=5  6x5=30  30—6=5 

6  +  6=12  12-6=6  6x6=36  36-6=6 

EQUAL  PARTS  OF  NUMBERS. 

•J-  of    6  =  1  £  of  18  =  3  |  of  30  =  5 

|  of  12  =  2  £  of  24  =  4  £  of  36  =  6 

When  the  regular  Jorm  of  each  table  has  been  thoroughly 
learned,  require  the  pupil  to  reverse  the  order  of  the  numbers ; 
thus,  in  Addition,  for  2  +  6=8,  say  6  +  2=8;  in  Subtraction,  for 
8-6=2,  say  8-2=6;  in  Multiplication,  for  6x2=12,  say  2x6 
=12  ;  and  in  Division,  for  12-*-6=2,  say  12-^-2=6,  etc. 


IK     ARITHMETIC.  59 

LESSON    XLVIII. 

1.  If  a  man  have  18  dollars,  and  he  earn  6  more,  how 
many  dollars  will  he  then  have  ?     18  +  6=  ? 

2.  A  man  having  18  dollars  gave  6  dollars  for  a  barrel 
of  flour.     How  many  dollars  had  he  left  ?     18  —  6=  ? 

3.  A  laborer  received  3  dollars  a  day  for  6  days  woi  k. 
How  many  dollars  did  he  receive  in  all  ?    3  x  6  =  ? 

4.  At  3  dollars  apiece,  how  many  chairs  can  be  bought 
for  18  dollars  ?     18-=-6=  ? 

EXERCISES  FOE  THE  SLATE  AND  BOARD. 

5.  Write  the  proper  numbers  in  place  of  (?): 


10  +  6=? 

13  +  6=? 

15  +  6=? 

23  +  6=? 

10—6=  ? 

13  —  6=  ? 

15  —  6=  ? 

22  —  6=? 

4x6=? 

5x6=? 

3x6=? 

6x6=? 

12-f-6=? 

18-f-6=? 

30-^-6=? 

36^-6=? 

Addition. 

3        4 

443 

643 

4        6 

4        5 

645 

434 

3         4 

6        3 

556 

456 

5         3 

Subtraction. 

9      10      12       10        7      12       11       10      13        9 

^J^_SJ>_1-1_1_1-1_?. 
Multiplication. 

6356445666 
4655646346 

Division. 

6)24   5)25    4)16    6)18   4)24    6)36 


60  FIRST     BOOK 

LESSON    XLJX. 

1.  How  many  are  3  and  4  ?    4  and  3  ?    5  and  2  ? 

2.  How  many  are  7  and  1  ?     7  and  2  ?     7  and  3  ? 

3.  How  many  are  7  and  5  ?     7  and  6  ?     7  and  7  ? 

4.  How  many  are  14  and  7  more  ?     14  +  7=  ? 

5.  Count  21  by  3's.     Count  21  by  7's. 

6.  How  many  are  21  and  7  more  ?     21  +  7=  ? 

7.  Count  28  by  2's.    Count  28  by  4's.    Count  28  by  7's. 

8.  Count  35  by  5's.     Count  35  by  7's. 

P.  How  many  are  35  less  7  ?    28  less  7  ?    21  less  7  ? 

10.  How  many  are  35  and  7  more  ?    42  and  7  more  ? 

11.  Count  42  by  2's.     By  3's.     By  6's.     By  7's. 

12.  How  many  are 

7  +  7  +  7?  7  +  7  +  7  +  7?  7  +  7  +  7  +  7  +  7? 
IS.  How  many  are 

35-7?  28-7?  21-7?  14-7?  7—7? 
14-  How  many  are 

7x2?   7x3?   7x4?  7x5    7x6? 

15.  How  many 

7's  in  21?      7's  in  28?      7's  in  35?      7's  in  42? 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 

16.  Copy  and  add  or  count  the  following  : 

7777777756 
7777777672 
7654321137 

When  the  pupil  can  rapidly  and  accurately  add  three  figures  in 
a  column,  the  number  of  figures  should  be  increased  to  four,  then 
five,  then  six,  and  then  to  seven. 


INABITHMETIC.  61 

LESSON    L. 

1.  If  21  yards  of  cloth  are  made  into  7  coats  of  the 
same  size,  into  how  many  equal  parts  must  the  21  yards 
be  cut  ? 

2.  When  a  number  is  divided  into  7  equal  parts,  what  is 
one  of  the  parts  called?     One-seventh  of  the  number. 

3.  How  many  yards  are  one-seventh  of  21  yards  ? 

O  O  0  O  O  O  0 

00        00        00        00        00        00  00 

21  -f-  7  =  3,        or    one-seventh  of  21  is  3. 

4.  How  many  birds  are  one-seventh  of  7  birds  ?    Of 
14  birds  ?     Of  21  birds  ? 

5.  If  21  bushels  of  apples  are  put  into  7  barrels,  what 
part  of  the  21  bushels  is  put  into  1  barrel  ?    How  many 
bushels  ? 

6.  One-seventh  is  written  thus,  -3J-.     |  of  28  is  28-;-  7 =4. 

TABLES. 
ADDITION. 

0  +  7=7  3  +  7=10  6  +  7=13 

1  +  7=8  4+7=11  7  +  7=14 

2  +  7=9  5  +  7=12  8  +  7=15 

SUBTRACTION. 

7-7=0  10-7=3  13-7=6 

8—7=1  11  —  7=4  14—7=7 

9-7=2  12-7=5  15-7=8 

MULTIPLICATION. 

7x0=  0  7x3=21  7x6=42 

7x1=  7  7x4=28  7x7=49 

7x2=14  7x5=35  7x8=56 


62  FIRST     BOOK 

LESSON    LI. 

TABLES —  Continued. 

DIVISION. 

0—7=0                21-^7=3  42^7=6* 

7-7=1                28^-7=4  49-f-7  =  7 

14-n7= 2                35-^-7=5  56-i-7=8 

EQUAL  PARTS  OF  NUMBERS. 

|  of    0=0             }•  of  21=3  |  of  42  =  6 

|  of    7=1             |  of  28=4  |  of  49  =  7 

|  of  14=2             |  of  35=5  i  of  56=8 

How  many  are 

7  times  5  boys  ?  5  times  7  coats  ? 

3  times  7  pears  ?  7  times  7  cents  ? 

7  times  6  hats  ?  4  times  7  horses  ? 

How  many  are 

|  of  14  roses  ?  |  of  25  miles  ? 

|  of  28  dollars  ?  |  of  42  oranges  ? 

•i-  of  21  pounds  ?  |  of  49  days  ? 

Addition  at  Siyht. 

4657773077 
7773677754 

Subtraction  at  Sight. 

7      10      13      12        7      14      21        9        7        7 

J^_Z_!J^J:_l_!_!JlJl 

Multiplication  at  Sight. 

7267477757 
3775724677 


ARITHMETIC. 


63 


LESSON    LIL 

1.  John  gave  5  cents  for  a  pencil,  4  cents  for  a  top, 
and  had  2  cents  left.     How  many  cents  had  he  in  all  ? 

2.  There  were  35  sheep  in  a  lot  and  7  jumped  out. 
How  many  remained  ? 

8.  What  will  be  the  cost  of  6  papers  of  needles,  at 
7  cents  a  paper  ? 

4.  How  many  pounds  of  rice  can  be  bought  for  42 
cents,  at  7  cents  a  pound  ? 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 

5.  Write  the  proper  numbers  in  place  of  (?). 


21  +  7=? 
21-7=? 
3x7=? 
21-7-7-  ? 

28  +  7=? 
28-7=? 
5x7=? 
28-f-7=? 

14  +  7=? 
42—7=  ? 
6x7=? 
35-7-7==? 

29  +  7=? 

29—7=  ? 
7x7=? 
42-=-7=  ? 

Addition. 

7 

5 

4 

3 

6 

7 

4 

7 

6 

7 

7 

7 

6 

7 

0 

1 

5 

3 

7 

7 

6 

4 

7 

7 

7 

6 

6 

6 

7 

7 

9      10      11 


14      13      12      17 


11 

6 


12 
5 


Multiplication. 

7740 
3'577 


7 
6 


7)14      6)24      7)28      5)30      7)35      6)36 


64  FIKSTBOOK 

LESSON     LIIL 

L  How  many  are  7  and  1?  6and2?  5and3?  4and4? 

2.  How  many  are  8  and  5?  8  and  6?  8  and  7?  8and8? 

S.  Count  16  by  2's.     By  4's.     By  8's. 

4.  How  many  are  16  and  8  more  ?     16  +  8=  ? 

5.  Count  24  by  2's.     By  4's.     By  6's.     By  8's. 

6.  How  many  are  24  and  8  more  ?    24  +  8=  ? 

7.  Count  32  by  2's.     By  4's.     By  8's. 

8.  How  many  4's  in  32  ?    How  many  8's  ? 

P.  How  many  are  32  less  8  ?    24  less  8  ?    16  less  8  ? 

10.  How  many  are  32  and  8  more  ?    32  +  8=  ? 

11.  Count  40  by  2's.     By  4's.     By  5's.     By  8's. 

12.  How  many  are  40  and  8  more  ?    48  and  8  more  ? 

13.  How  many  8's  in  40  ?    How  many  5's  ? 
14*  How  many  are 

8+8+8?       8+8+8+8?       8+8+8+8+8? 
IB.  How  many  are 
40—8?      32—8?      24—8?      16—8?      8—8? 

16.  How  many  are 

8x2?     8x3?     8x4?    8x5?    8x6?    8x7? 

17.  How  many  are 

8-5-8?      16-f-S?      24-5-8?      32-~8?      40-^8? 

•     EXEECISES   FOR  THE   SLATE   AND   BOARD. 

18.  Copy  and  add  or  count  the  following  : 

8888888843 
8888888858 
8888888862 
8765432187 


IN     AEITHMETIC.  65 

LESSON     LIV. 

1.  If  32  pounds  of  tea  are  put  into  8  boxes,  an  equal 
number  of  pounds  into  each  box,  into  how  many  equal 
parts  are  the  32  pounds  divided  ? 

2.  When  a  number  is  divided  into  8  equal  parts,  what  is 
one  of  the  parts  called  ?      One-eighth  of  the  number. 

3.  How  many  pounds  are  one-eiglith  of  32  pounds  ? 

@J9      ®J9      ^      @©      @©      @J9      @©  @JB 

®"a      <^B      ^D      65©      @®      ©©      GOB  .  6/B 

32  -f  8  =  4,        or    one-eighth  of  32  is  4 

^.  How  many  are  one-eighth  of  16  men  ?     Of  24  men  ? 

5.  If  40  boys  sit  upon  8  benches,  on  each  an  equal 
number,  what  part  of  the  40  boys  sit  upon  1  bench  ? 
How  many  boys  ? 

6.  One-eighth  is  written  thus,  £.     $  of  48  is  48—8=6. 

TABLES. 


ADDITION. 

0+8=  8 

3  +  8  =  11 

6  +  8  =  14 

1  +  8=  9 

4  +  8=12 

7  +  8  =  15 

2  +  8=10 

5  +  8=13 

8  +  8  =  16 

SUBTRACTION. 

8-8=0 

11_8=  3 

14—8  =  6 

9-8=1 

12-8=4 

15-8  =  7 

10—8=2 

13_8  =  5 

16-8=8 

MULTIPLICATION. 

8x0=  0  8x3=24  8x6=48 

8x1=  8  8x4=32  8x7=56 

8x2=16  8x5=40  8x8=64 


66  FIEST    BOOK 

LESSON     LV. 


TABLES  —  Continued. 

DIVISION. 

0-8=0 

24^-8=3 

48^-8=6 

8-8=1 

32^-8=4 

56^-8=7 

16-8=2 

40-8=5 

64—8=8 

EQUAL  PAKTS. 

to*    0=0 

£  of  24=3 

^  of  48=6 

iof    8=1 

£  of  32=4 

-i  of  56  =  7 

4  of  16=2 

4  of  40=5 

4  of  64=8 

How  many  are 

8  times  3  eggs  ?  6  times  8  hours  ? 

5  times  8  nuts  ?  8  times  8  cents  ? 

8  times  4  pins  ?  7  times  8  quarts  ? 

How  many  are 

-J  of  24  miles  ?  -J-  of  48  men  ? 

£  of  16  dollars  ?  i  of  56  bushels  ? 

%  of  32  ounces  ?  £  of  40  cents  ? 

Addition  at  Sight. 

8858473868 
6788888584 

Subtraction  at  Sight. 

8      10      12      16        9        8        8      24      14      11 
8888831888 


Itf    ARITHMETIC.  67 

LESSON    LVI. 

1.  Kobert  found  16  ripe  peaches  under  a  tree  ;  he  ate 
3  and  gave  away  5.     How  many  had  he  left  ? 

2.  George  had  24  cents,  which  was  8  more  than  Ella 
had.    How  many  cents  had  Ella  ? 

3.  At  8  cents  each,  what  is  the  cost  of  6  writing-books  ? 

4.  At  8  cents  a  yard,  how  many  yards  of  ribbon  can  be 
bought  for  48  cents  ? 

EXERCISES  FOE  THE  SLATE  AND  BOAKD. 

5.  Write  the  proper  numbers  in  place  of  (?): 

16  +  8=?  15  +  8=?  32  +  8=?  22  +  8=? 

16—8=?  15—8=?  32—8=?  22—8=? 

7x8=?  5x8=?  8x8=?  6x8=? 

24-^-8=  ?          40-r-8=  ?  48^-8=  ?  56-r-8=  ? 


Addition. 

8 

7 

5 

6 

4 

4 

8 

8 

8 

7 

5 

1 

8 

8 

0 

6 

3 

6 

8 

7 

3 

4 

6 

8 

8 

7 

2 

7 

8 

8 

Subtraction. 

9       11       12        8       16       14      24      15       12      10 

_?_^_?_^_l_l_iJLA_i 

Multiplication. 

8765487788 
3548766778 

Division. 

6)18  8)56  8)40  7)49  6)48 


68  FIRST     BOOK 

LESSON     LVII. 

1.  How  many  are  8  and  1?  7and2?  6and3?  5and4? 

2.  How  many  are  9  and  7  ?     9  and  8  ?     9  and  9  ? 
S.  Count  18  by  2's.     By  3's.     By  6's.     By  9's. 

4.  Count  27  by  3's.     Count  27  by  9's. 

5.  How  many  3's  in  27  ?     How  many  9's  in  27  ? 

6.  How  many  are  27  less  9  ?     18  less  9  ?     9  less  9  ? 

7.  Count  36  by  2's.    By  3's.    By  4's.    By  6's.    By  9's. 

8.  How  many  are  36  less  9  ?     27  less  9  ?     18  less  9  ? 

9.  Count  45  by  3's.     By  5's.     By  9's. 

10.  How  many  5's  in  45  ?     How  many  9's  ? 

11.  How  many  are  45  and  9  more  ?    45  +  9=  ? 

12.  How  many  are  54  and  9  more  ?     54+  9=  ? 
18.  Count  63  by  3's.     By  7's.     by  9's. 

14.  How  many  7's  in  63  ?     How  many  9's  ? 

15.  How  many  are 

9+9+9?         9+9+9+9?         9+9+9+9+9? 

16.  How  many  are 

63-9?       54-9?      45-9?      36-9?       18-9? 

17.  How  many  are 

9x3?         9x4?         9x5?         9x6?        9x7? 

18.  How  many  are 

18-^9?    27-5-9?    36^9?     45^-9?     54-^-9?     63-^-9? 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 

19.  Copy  and  add  or  count  the  following  : 

999-9999999 
9999999999 
98  76543  2. IQ 


IK     ARITHMETIC. 

LESSON    LVIII. 

1.  If  45  trees  are  set  in  9  rows,  an  equal  number  in 
each  row,  into  how  many  equal  parts  are  the  45  trees 
divided  ? 

2.  When  a  number  is  divided  into  9  equal  parts,  what 
is  one  of  the  parts  called  ?     One-ninth  of  the  number. 

8.  How  many  trees  are  one-ninth  of  45  trees  ? 


45  -7-  9  =  5,         or    one-ninth  of  45  is  5. 

4.  flow  many  rods  are  one-ninth  of  9  rods  ?     Of  18 
rods  ?     Of  36  rods  ? 

5.  If  27  bushels  of  grain  be  put  into  9  bags  of  equal 
size,  what  part  of  the  27  bushels  .will  1  bag  contain  ? 
How  many  bushels  ? 

6.  One-ninth  is  written  thus,  ^.    ^  of  54  is  54—9=6. 

TABLES. 
ADDITION. 

1  +  9=10  4  +  9=13  7  +  9  =  16 

2  +  9  =  11  5  +  9  =  14  8  +  9=17 

3  +  9  =  12  6  +  9  =  15  9  +  9  =  18  ' 

SUBTRACTION. 

10—9  =  1                13  —  9=4  16  —  9  =  7 

11—9=2                14—9=5  17—  9=8 

12—9=3                15  —  9  =  6  18—9  =  9 

MULTIPLICATION. 

9x1=  9                9x4=36  9x7=63 

9x2  =  18                9x5=45  9x8  =  72 

9x3=27                9x6=54  9x9=81 


70  FIRST     BOOK 

LESSON    LIX. 


TABLES  —  Continued. 

DIVISION. 

9-r-9  =  l 

36-f-9=4 

63-f-9  =  7 

18-r-9=2 

45-^-9=5 

72-5-9=8 

27-f-9=3 

54-r-9  =  6 

81  —  9=9 

EQUAL  PARTS. 

|of    9=1 

i  of  36=4 

i  of  63  =  7 

i  of  18=2 

i  of  45  =  5 

|  of  72=8 

£  of  27=3 

i  of  54=6 

i  of  81  =  9 

How  many  are 

9  times  4  balls  ?  8  times  9  miles  ? 

6  times  9  boxes  ?  9  times  7  feet  ? 

9  times  5  hens  ?  9  times  9  cents  ? 

How  many  are 

i  of  27  sheep  ?  |  of  63  gallons  ? 

•J-  of  36  acres  ?  $  of  72  girls  ? 

$  of  54  boys  ?  |  of  81  marbles  ? 

Addition  at  Siylit. 

9978499959 
5699937899 

Subtraction  at  Sight. 

10        9      11       12        9       18      27      26      14       15 


In  all  the  foregoing  tables,  the  pupil  should  be  required  to  invert 
the  order  of  the  numbers,  and  to  repeat  them  backward  and  pro- 
miscuously until  they  are  thoroughly  memorized. 


IN     ARITHMETIC.  71 

LESSON     LX. 

1.  In  a  garden  are  18  pear  trees  and  9  peach  trees. 
How  many  of  both  ?    How  many  more  pear  trees  than 
peach  trees  ? 

2.  There  are  6  peaches  on  each  tree.     How  many 
peaches  on  the  9  trees  ? 

3.  At  9  cents  a  pound,  how  many  pounds  of  sugar  can 
be  bought  for  45  cents  ?    For  54  cents  ?     For  27  cents  ? 

4.  How  many  are  one-ninth  of  18  books?  Of  36  melons? 

EXERCISES  FOE  THE  SLATE  AND  BOARD. 

5.  Write  the  proper  numbers  in  place  of  (?). 


27  +  9=? 

36  +  9=  ? 

63  +  9=? 

27—9=? 

36-9=? 

63-9=? 

3x9=? 

5x9=? 

8x9=? 

27^9=? 

45-7-9=? 

72-5-9=? 

c 

Addition. 

7 

8        7 

9 

9         8 

9 

6        8 

9 

3 

2         9 

5 

9        7 

3 

6        8 

9 

9 

9         4 

2 

4        9 

9 

8        8 

9 

Subtraction. 

12       35        9       16       18      27      29       17      16        9 

_!_^_!_^J^_^Ii_^_!_i 

Multiplied  tion. 

7896798899 
8659879869 

Division. 

9)27    6)54    9)63    9)72    9)81    7)63 


FIKSTBOOK 

LESSON     LXI. 

1.  How  many  are  9  and  1  ?  7  and  3?  6  and  4?  5  and  5? 

2.  How  many  are  10  and  5  ?     10  and  7  ?     10  and  8  ? 

8.  Count  by  2's  to  20.     By  4's.     By  5's.     By  10's. 

If.  How  many  2's  in  20  ?   How  many  4's  ?  5's  ?   10's  ? 

5.  How  many  are  20  and  10  more  ?    20  +  10=  ? 

6.  How  many  are  30  and  10  ?  40  and  10  ?  50  and  10  ? 

7.  How  many  10's  in  30  ?     In  40  ?     In  50  ?  .  In  60  ? 
8..  Count  40  by  2's.    By  4's.    By  5's.   By  8's.   By  10's. 

9.  Count  by  10's 

From  1  to  91.  From  6  to    96. 

From  2 -to  92.  From  7  to    07. 

From  3  to  93.  From  8  to    98. 

From  4  to  94.  From  9  to    99. 

From  5  to  95.  From  0  to  100. 

10.  How  many  are 

10  + 10  +  10 -f  10?         10  +  10  +  10  +  10  +  10? 

11.  How  many  are 

100—10?        90—10?        70—10?       40—10? 

12.  How  many  are 

10  x  5  ?     10  x  7  ?     10  x  6  ?     10  x  8  ?    10  x  10  ? 
18.  How  many  are 

40-4-10?     504-10  i     704-10?     804-10?     904-10? 
IJf.  When  a  number  is  divided  into  10  equal  parts,  what 
is  one  of  the  parts  called  ?     One-tenth  of  the  number. 

15.  How  many  barrels  are  one-tenth  of  70  barrels  ? 

70  4-  10  =  7,       or    one-tenth  of  70  is  7. 

16.  How  many  sheep  are  one-tenth  of  80  sheep  ? 

17.  One-tenth  is  written  thus,  -fa.  -^  of  90  is  904-10=9. 


IN-     ARITHMETIC. 


LESSON    LXII. 

TABLES. 

ADDITION. 

0  +  10=10 

4  +  10  =  14 

8  +  10=18 

1  +  10  =  11 

5  +  10  =  15 

9  +  10=19 

2  +  10=12 

6  +  10  =  16 

*10  +  10=20 

3  +  10=13 

7  +  10=17 

11  +  10=21 

SUBTRACTION. 

10—10=0 

14—10  =  4 

18-10=  8 

11-10=1 

15_10  =  5 

19-10=  9 

12-10=2 

16  —  10  =  6 

20  —  10=10 

13  —  10=  3 

17_10  =  7 

21—10=11 

MULTIPLICATION. 

10x0=  0 

10x4=40 

10  x   8=  80 

10x1  =  10 

10x5  =  50 

10  x    9=  90 

10x2=20 

10x6  =  60 

10x10=100 

10x3=30 

10x7  =  70 

10x11  =  110 

DIVISION. 

0—10=0 

40-10=4 

80-f-10=  8 

10—10=1 

50—10=5 

90-^-10=  9 

20-10=2 

60-10=6 

100-r-10=10 

30-10=3 

70—10=7 

EQUAL  PARTS. 

•3*5-  of    0=0 

-^  of  40=4 

iVof    80=  8 

^o-  of  10=1 

^  of  50  =  5 

^of    90=  9 

^  of  20=2 

^  of  60  =  6 

-iV  of  100=10 

^  of  30=3 

^  of  70=7 

74  FIRST     BOOK 

LESSON     LXIII. 

1.  How  many  are  10  and  1  ?    8  and  3  ?    9  and  2  ? 
7  and  4  ?     6  and  5  ? 

2.  How  many  are  11  and  4  ?     11  and  6  ?     11  and  9  ? 

3.  How  many  are  11  and  *7  ?   11  and  10  ?   11  and  11  ? 

4.  Count  by  2's  to  22.    How  many  2's  in  22  ?    How 
many  ll's  in  22? 

5.  How  many  are  22  and  11  more  ?    22  +  11=  ? 

6.  How  many  are  33  and  11  more  ?    33  +  11=  ? 

7.  How  many  are  44  and  11  more  ?     55  and  11  ? 

8.  How  many  ll's  in  33  ?    In  44  ?     In  55  ?     In  66  ? 

9.  Count  44  by  2's.     By  4's.     By  ll's. 

10.  How  many  are  66  + 11  ?  77  + 11  ?  88  + 11  ?  99  + 11  ? 

11.  How  many  are 

99-11?       88-11?       77-11?       66-11?      77-11? 

12.  How  many  are 

11x2?     11x3?     11x4?     11x5?     11x6?     11x7? 

13.  How  many  are 

88-f-ll?       77-r-ll?    *   66-7-11?       55-hll?       44—11? 

14.  When  a  number  is  divided  into  11  equal  parts, 
what  is  one  of  the  parts  called  ? 

One-eleventh  of  the  number. 

15.  How  many  boys  are  one-eleventh  of  44  boys  ? 

44  -^  11  =  4,      or   one-eleventh  of  44  is  4. 

16.  How  many  days  are  one-eleventh  of  55  days  ? 

17.  One-eleventh  is  written  thus,  ^.    -^  of  66  is  66 ~- 
11  =  6. 

IS.  If  88  cents  are  divided  among  11  boys,  what  part 
of  the  whole  does  each  boy  receive  ?     How  many  cents  ? 


ARITHMETIC. 


75 


LESSON    LXIV. 


TABLES. 

ADDITION. 

0  +  11  =  11 

4  +  11  =  15 

8  +  11  =  19 

1  +  11=12 

5  +  11  =  16 

9  +  11  =  20 

2  +  11  =  13 

6  +  11  =  17 

10  +  11=21 

3  +  11=14 

7  +  11  =  18 

11  +  11=22 

SUBTRACTION. 

11-11=0 

15  —  11=4 

19—11=  8 

12—11=1 

16-11  =  5 

20-11=  9 

13-11=2 

17-11  =  6 

21  —  11  =  10 

14—11=3 

18  —  11  =  7 

22-11=11 

MULTIPLICATION. 

11x0=  0 

11x4=44 

11  x   8=  88 

11x1  =  11 

11x5  =  55 

11  x   9=  99 

11x2=22 

11x6  =  66 

11x10=110 

11x3=33 

11x7  =  77 

11x11=121 

DIVISION. 

0—11=0 

44—11  =  4 

88—11=  8 

11-11  =  1 

55  —  11  =  5 

99—11=  9 

22—11=2 

66  —  11  =  6 

110—11=10 

33-11=3 

77—11  =  7 

121—11=11 

EQUAL  PARTS. 

^of    0=0 

^  of  44=4 

•fr  of    88=  8 

^  of  11  =  1 

•j^-  of  55=5 

-^  of    99=  9 

-^  of  22  =  2 

-&  of  66  =  6 

TV  of  110=10 

A  of  33=3 

TV  of  77=7 

A-  of  121=11 

FIKST     BOOK 


LESSON    LXV. 

1.  How  many  are  11  and  1  ?    8  and  4  ?     9  and  3  ? 

2.  What  numbers  multiplied  together  will  produce  12  ? 

3.  How  many  are  12  and  4  ?     12  and  6  ?     12  and  8  ? 

4.  How  many  are  12  and  9  ?    12  and  10  ?    12  and  12  ? 

5.  Count  by  2's  to  24.  By  4's.  By  6?s.  By  8's.  By  12's. 

6.  How  many  are  24  and  12  more  ?     24  + 12=  ? 

7.  How  many  are  36  and  12  more  ?    36  + 12=  ? 

8.  How  many  squares  in  one  row  ? 
How  many  12's  ? 

9.  How    many    squares    in    two 
rows  ?    How  many  12's  ? 

10.  How  many  squares  in   three 
rows?     How  many  12's  ? 

11.  How  many  squares  in  4  rows  ? 

12.  In  5  ?   In  6  ?   In  7  ?   In  8?   In  10?  In  11  ?  In  12? 

13.  What  is  |  of  12  ?    £  of  12  ?    £  of  12  ?    $  of  12  ? 

14.  How  many  12's  in  24  ?     In  36  ?     In  48  ?     In  60  ? 

15.  Count  60  by  3's.    By  5's.   By  6?s.   by  10's.  By  12's. 
How  many  are 

16.  36  +  12?    48  +  12?    60  +  12?     72  +  12?    84  +  12? 

17.  96-12?     84-12?     72-12?    60-12?    48-12? 

18.  12x2?     12x3?-    12x4?     12x5?     12x6? 

19.  How  many  are  24-^12?  36-^12?  48-f-12?  60-7-12? 

20.  When  a  number  is  divided  into  12  equal  parts,  what 
is  one  of  the  parts  called  ?  One-twelfth  of  the  number. 

21.  How  many  eggs  are  one-tivelfth  of  60  eggs  ? 

60  -r- 12  =  5,       or  one-twelfth  of  60  is  5. 

22.  One-twelfth  is  written  ^.     ^  of  72  is  72-4-12  =  6. 


ARITHMETIC. 


LESSON    LXVI. 


TABLES. 

ADDITION. 

1  +  12=13 
2  +  12=14 
3  +  12  =  15 

5  +  12  =  17 
6  +  12  =  18 
7  +  12  =  19 

8  +  12=20 

9  +  12=21 
10  +  12=22 
11  +  12=23 
12  +  12=24 

SUBTRACTION. 

13-12=1 
14—12=2 

16-12=4 

17_12=5 
18-12  =  6 
19  —  12  =  7 
20-12=8 

21-12=  9 
22—12=10 
23-12  =  11 
24-12=12 

MULTIPLICATION. 

12x1  =  12- 
12x2=24 
12x3=36 
12x4=48 

12x5  =  60 
12x6  =  72 
12x7  =  84 
12x8  =  96 

12  x    9  =  108 
12x10=120 
12x11  =  132 
12x12  =  144 

DIVISION. 

12-4-12  =  1 
24-r-12=2 
36-^12=3 
48-4-12=4 

60-^-12=5 
72-4-12  =  6 
84-5-12==  7 

96-=-12=8 

108-4-12=  9 
120-4-12=10 
132-4-12=11 
144-^12  =  12 

•fg  of  12  =  1 
-^  of  24=2 
^  of  36=3 
&  of  48=4 

EQUAL  PARTS. 
-^  of  60  =  5 
•&  of  72  =  6 
A-  of  84=7 
A  of  96=8 

•fy  Of   108=     9 

&  of  120  =  10 
&  of  132=11 
A-  of  144=12 

78 


FIBST     BOOK 


ONE    HUNDRED. 

LESSON    LXVII. 

1.  How  many  rows  of  blocks  are  shown  in  this  picture  ? 

2.  How  many  blocks  in  each  row  ?    How  many  blocks 
in  all? 

3.  Ten  times  10  blocks  are  how  many  ?    10  x  10—  ? 

4.  How  many  10's  in  one  hundred  ?    How  many  units  ? 
6.  Count  from  1  to  100  by  10's.     From  5.     From  7. 

6.  Write  the  figures  that  stand  for  one  hundred.    100 

7.  How  then  do  we  express  one  hundred  in  figures  ? 

8.  What  does  1  denote  when  it  stands  alone  ? 

9.  What  does  it  denote  with  one  0  on  the  right  of  it  ? 

10.  What  does  it  denote  with  two  00  on  the  right  of  it  ? 

11.  Hence,  we  represent  2  tens  or  twenty,  by  20  ;  and 

12.  20  tens  or  Two  hundred,  by  200. 
18.     30  tens  or  Three  hundred,  by  300. 
H.     40  tens  or  Four  hundred,  by  400. 

15.  50  tens  or  Five  hundred,  by  500. 

16.  60  tens  or  Six  hundred,  by  600. 

17.  70  tens  or  Seven  hundred,  by  700. 

18.  80  tens  or  Eight  hundred,  by  800. 

19.  90  tens  or  Nine  hundred,  by  900 


ARITHMETIC. 


ONE    HUNDRED    and    FIFTY-  SIX.       156. 

LESSON    LXVIII. 

1.  Any  figure  standing  alone  is  units;   thus,  6  is 
6  units. 

2.  When  two  figures  are  written  together,  the  one  on 
the  right  is  units,  the  one  on  the  left  is  tens;  thus,  56 
is  5  tens  or  fifty,  and  6  units,  and  is  read,  fifty-six. 

3.  When  three  figures  stand  together,  the  one  on  the 
right  is  units,  the  next  figure  is  tens,  and  the  third  on 
the  left  is  hundreds  ;  thus,  156  is  1  hundred,  5  tens 
and  6  units,  read  one  hundred  fifty -six. 

4.  What  do  the  figures  243  denote  ? 

Ans.  2  hundreds,  4  tens,  and  3  units,  and  is  read  two 
hundred  forty-three. 

5.  What  do  the  figures  427  denote  ? 

6.  Copy  and  ^ead  the  following,  naming  the  hundreds, 
tens,  and  units  in  each. 

341     184     537     782     872 
462     265     673     394     935 


80  FIRST     BO OK 

LESSON     LXIX. 

1.  How  many  units  in  100  ?     How  many  tens  9    How 
many  hundreds  9 

2.  How  many  units  in  200  ?     How  many  tens  ?    How 
many  hundreds  ? 

3.  How  many  units  in  300  ?  In  400  ?  In  500  ?  In  600  ? 

4.  How  many  tens  in  300  ?  In  400  ?  In  500  ?  In  600  ? 

5.  How  many  hundreds  in  300  ?     In  400  ?     In  500  ? 
5.  How  many  tens  in  210  ?    In  220  ?  In  340  ?  In  450  ? 
7.  How  many  units  in  225  ?     How  many  te/zs  and 

units  9    How  many  hundreds,  tens,  and  %mYs  ? 
6*.   10  units  =  1  ten  :  10  tens  =  1  hundred. 

9.  When  no  number  is  named  for  any  place,  fill  the 
place  with  a  cipher;  thus,  seven  hundred  six  is  7  hun- 
dred, no  tens,  and  6  units,  and  is  written     706. 

10.  Seven  hundred  eighty  is  written         780. 

11.  Copy  and  read  the  following,  naming  the  number 
of  hundreds,  tens,  and  units  in  each. 

563  287  301  804  203 

409  640  711  650  105 

12.  Write  the  following  numbers  in  figures,  and  name 
the  hundreds,  tens,  and  units  in  each. 

18.  Seven  hundred  eight. 

14.  Five  hundred  sixty. 

15.  Three  hundred  eighty-seven. 

16.  One  hundred  ninety-five. 
11.  Eight  hundred  seven. 

18.  Six  hundred  fourteen. 

19.  Four  hundred  sixteen. 


Itf     ARITHMETIC.  81 

LESSON    LXX. 

1.  In  what  place  are  units  written  ?     Tens  ?     Hun- 
dred? 

2.  How  many  units  make  one  ten  ? 

3.  How  many  tens  make  one  hundred  ? 

4-  How  many  units  are  7  tens  and  9  units  ? 

5.  How  many  tens  are  4  tens  and  5  tens  ? 

6.  How  many  hundred  are  3  hundred  and  4  hundred  ? 
How  many  tens  ?     How  many  units  ? 

Express  in  one  number,  by  figures,  each  of 
ths  following  : 


7.  4  tens,  6  units,  and  5  hundred. 

8.  5  units,  8  hundred,  and  4  tens. 

9.  Six  hundred,  eight  units,  and  five  tens.  G 

10.  Seven  tens,  no  hundreds,  and  six  units.  0 

11.  Four  units,  no  tens,  and  five  hundred.  5 

12.  Nine  tens,  seven  hundred, and  no  units.  (  7 


Write  the  following  numbers  in  columns,  placing 
units  under  units,  tens  under  tens,  and  hundreds  under 
hundreds  : 

18.  366,  48,  104,  261,  407,  39,  and  7. 

14.  59,  116,  204,  16,  320,  40,  and  10. 

15.  What  is  the  greatest  number  that  can  be  expressed 
by  one  figure  ? 

16.  What  is  the  greatest  number  that  can  be  expressed 
by  two  figures  ? 

17.  The  greatest  number  that  can  be  expressed  by  three 
figures  is  999. 

18.  999  and  1  more  equal    One  thousand. 


FIEST     BOOK 


ONE    THOUSAND. 

LESSON    LXXL 

1.  How  many  are  10  times  10  ? 

2.  In  the  picture  there  are  100  small  blocks  in  the  top 
row  or  layer.    How  many  hundred  blocks  are  there  in 
2  rows  or  layers  ? 

8.  How  many  hundred  blocks  in  3  rows  ?     In  4  rows  ? 

4.  How  many  in  5  rows  ?     In  6  rows  ?     In  7  rows  ? 
In  8  rows  ?     In  9  rows  ?     In  10  rows  ? 

5.  Ten  hundred  equals  one  thousand. 

6.  One  thousand  is  written  thus  :  1,000 

7.  What  does  1  with  three  OOO's  on  the  right  denote  ? 

8.  In  like  manner  are  represented, 


Two  thousand,  by  2,000. 

Three  thousand,  by  3,000. 

Four  thousand,  by  4,000. 

Five  thousand,  by  5,000. 


Six  thousand,  by  6,000. 
Seven  thousand,  by  7,000. 
Eight  thousand,  by  8,000. 
Nine  thousand,  by  9,000. 


9.  In  any  number  expressed  by  four  figures,  the  figure 
at  the  right  is  units,  the  next  is  tens,  the  next  hundreds, 
and  the  fourth  figure  from  the  right  is  thousands. 

Thus,  2345,  is  2  thousands,  3  hundreds,  4  tens,  5  units, 
and  is  read  two  thousand  three  hundred  forty-five. 


ARITHMETIC,, 


83 


LESSON     LXXII. 

L  What  do  the  figures  1040  denote  ? 
Ans.  1  thousand,  no  hundreds,  4  tens,  and  no  units, 
and  is  read  one  thousand  forty. 
2.  In  the  same  manner  copy  and  read  the  following  : 
2406          4051          3007          1904 
1572          5200          3333          6070 
Write  in  figures  the  following  numhers : 

3.  Three  thousand  five  hundred  seven. 

4.  One  thousand  two  hundred  ten. 

5.  Two  thousand  one  hundred  three. 

6.  Four  thousand  thirty. 

7.  Five  thousand  forty-six. 

8.  Seven  hundred  eight. 

9.  Five  hundred  ninety. 

10.  The  greatest  number  that  can  be  expressed  by  four 
figures  is  9999. 

11.  9999  and  1  more  equal  ten  thousand.  10 ,000 

12.  What  does  1  with  four  OOOO's  at  the  right  denote  ? 
In  like  manner  are  represented, 

13.  2  ten-thousands,  or  twenty  thousand,  by  20,000. 

14.  3  ten-thousands,  or  thirty  thousand,  by  30,000. 

15.  9  ten-thousands* or  ninety  thousand,  by  90,000,  etc. 

16.  10  units  make     1  ten. 


cc 

• 

. 

£j 

2 

02 

i^ 

O 

§ 

§ 

'3 

H 

a 

HP 

3 

5 

0 

7 

1 

2 

1 

0 

2 

1 

0 

3 

4 

0 

3 

0 

5 

0 

4 

6 

7 

0 

8 

5 

9 

0 

77.  10  tens 

18.  10  hundred 

19.  10  thousand 

£0.  10  ten-thousands 


1  hundred. 
1  thousand. 
1  ten-thousand. 
1  hundred  thousand. 
100,000 


84  FIRST     BOOK 

LESSON     LXXIII. 

1.  It  has  been  shown  that  the  same  figure  has  a  dif- 
ferent value,  according  to  its  place  from  the  right ;  thus, 
6  is  6  units,  60  is  6  tens,  600  is  6  hundreds,  etc. 

2.  The  different  places  are  sometimes  called  orders 
"of  units;  thus,  324  represents  4  units  of  ike  first  order, 

2  units  of  the  second  order,  or  2  tens,  and  3  units  of  the 
third  order,  or  3  hundreds. 

3.  The   different    orders    of   units   are  grouped  into 
periods  of  3  figures  each. 

4.  The  first  group  on  the  right  is  called  the  period  of 
units,  the  second,  the  period  of  thousands,  the  third,  the 
period  of  millions,  as  shown  in  the  following 

TABLE. 
PERIODS.         3d.  2d.  1st. 

f  «  ri 

NAME.  _?  & 

15  ^  tD 

ORDERS 


or 


3   a 


|     2    S    £  £53  3    S    S 

UNITS.    [  a  H  t>      H  H  P      MnP 
NUMBER.      127,       3^4,      549 

5.  This  number  is  read  one  hundred  and  twenty-seven 
million,  three  hundred  and  sixty-four  thousand,  five 
hundred  forty-nine. 

Each  period  is  read  like  a  number  of  three  figures, 
giving  it  the  name  of  the  period  ;  thus,  120,  120,  120  is 
120  million,  120  thousand,  120. 


IN     ARITHMETIC. 


85 


LESSON    LXXIV. 


cc 
+2 

'3 


2 


2 

1  4 
205 
040 


307 
460 
084 
602 
700 


To  assist  the  pupil  in  learning 
to  write  and  to  read  numbers 
readily,  he  may  be  required  to 
prepare  on  slate  or  paper,  or 
the  blackboard,  exercises  similar 
to  the  following. 

L  The  first  number  is  read, 
3  hundred  7. 

2.  The  second  is  read,  2  thou- 
sand 4  hundred  60. 

3.  The  third  is  read,  14  thousand  84. 

4.  The  fourth  is  read,  205  thousand  6  hundred  2. 

6.  The  5th  is  read,  2  million  40  thousand  7  hundred. 

When  proficiency  in  smaller  numbers  is  attained,  this  exercise 
may  be  extended  to  higher  periods. 

Copy,  point  off  into  periods,  and  read  the  following  : 

6.  3472;    5060;    17043;    20304;    600317;     108300. 

7.  500037  ;    2405037  ;     910307  ;     76301  ;     30406. 

8.  Write  the  preceding  numbers  in  columns,  placing 
units  under  units,  tens  under  tens,  etc. 

Write  in  figures,  arrange  in  columns,  point  off  and  read, 

9.  Nine  thousand  five  hundred  twelve;    twenty-two 
thousand  nine  hundred  forty;  sixty  thousand  four  hun- 
dred eight;  ten  thousand  one  hundred  fifteen. 

10.  One  hundred  twenty-five  thousand  three  hun- 
dred eleven  ;  three  hundred  seven  thousand  five 
hundred  four;  five  hundred  and  eleven  thousand 
fifteen. 


86 


FIRST     BOOK 


a  AUDI   lox 


LE 


LXXV. 


.7.  How  many  are  7  hats  and  5  hats  ?     6  boys  and  7 
boys  ?     8  men  +  9  men  ?     9  units  -f  7  units  ? 

2.  Can  you  add  6  books  and  4  dollars  ? 

3.  Why  not  ?     .^s.  Only  numbers  representing  things 
of  the  same  Icind  can  be  added. 

4-  How  many  units  in  9  tens  ?    In  7  tens  ?    In  8  tens  ? 

5.  How  many  tens  are  7  tens  and  5  tens  ?    How  many 
units  ? 

6.  How  many  hundreds  are  2  hundred  and  6  hundred  ? 
How  many  tens  ?     How  many  units  ? 

7.  How  many  tens  are  10  units  ?   30  units  ?   50  units  ? 

8.  How  many  hundreds  are  10  tens  ?  20  tens  ?  40  tens  ? 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 
1.  What  is  the  sum  of  34  and  53  ? 
4  =  3  tens  4  units. 


Numbers 
to  be 
added, 


\  3  =  5  tens  3  units. 

>  w i 

>  7  =  < 


Each  of  these  numbers  is 
made  up  of  tens  and  units. 
Adding  each,  the  sum  is  8 
tens  and  7  units,  or  87  units. 


Sum,  87  =  8  tens  7  units. 

In  similar  manner  add  the  following  : 

(2.)        (3.)        (4.)         (5.)        (6.)  (7.)  (8.) 

23         44          52          17          26  75  18 

55          32          27          71          52  23  60 


ARITHMETIC.  87 


LESSON     LXXVI. 

1.  I  paid  7  dollars  for  a  hat  and  9  dollars  for  a  vest ; 
how  many  dollars  did  I  pay  for  both  ? 

ANALYSIS. — I  paid  the  sum  <^jj^f^^  and  9  dollars,  which  is 
16  dollars. 


2.  A  farmer  sold  a  sheep  fo^BJ^j^and  a  calf  for 
8  dollars  ;  what  did  he  receive  for  1 

3.  A  hoy  had  16  marbles  and  his  mother  gave  him  5 
more  ;  how  many  marbles  had  he  then  ? 

4*  James  paid  6  cents  for  a  pencil,  5  cents  for  an 
orange,  and  8  cents  for  a  ball ;  what  did  he  pay  for  all  ? 
Find  the  sum  of 


5.  9,  7,  and  2. 

6.  5,  8,  and  4. 

7.  16,  4,  and  7. 


8.  8,  5,  and  7. 

9.  15,  5,  and  8. 
10.  21,  7,  and  5. 


11.  9,  10,  and  6. 

12.  8,  9,  and  10. 
18.  18,  6,  and  7. 


EXERCISES  FOR  THE  SLATE  AND  BOARD. 
1.  What  is  the  sum  of  324,  213,  and  431  ? 
Numbers  ,324  =  3  hunds.  2  tens  4  units.  Each  of    thege 

to  be     J  2  1  3  =  2  hunds.  1  ten    3  units.       numbers  is  made 
added,     (431  =  4  hands.  3  tens  1  unit.         up   of   hundreds, 

a «  Q  £  *       "Q  tens»  and  units. 

968  =  9  hunds.  o  tens  o  units. 

Adding  each,  the  sum  is  9  hundreds  6  tens  8  units,  or  968  units. 
In  a  similar  manner  add  the  following  : 

(*•)  (^)  (-*•)  (6.)  (6.) 

213  304  503  104  504 

425  123  172  302  670 

160  562  223  493  125 


88  FIRST     BOOK 

LESSON    LXXVII. 

The  following  are  all  the  combinations  that  can  be 
made  with  the  nine  digits,  except  with  the  unit  1,  up  to 
9  and  9  are  18. 


These  thoroughly  com^d  to  memory,  will  very  much  facili. 
fcate  the  adding  of  long  columns  with  ease  and  accuracy. 

2  and  2  are    4  *     4  and  7  are  11 

2  and  3  are    5  4  and  8  are  12 

2  and  4  are     6  4  and  9  are  13 

2  and  5  are     7  5  and  5  are  10 

2  and  6  are     8  5  and  6  are  11 

2  and  7  are     9  5  and  7  are  12 

2  and  8  are  10  5  and  8  are  13 

2  and  9  are  11  5  and  9  are  14 

3  and  3  are     G  6  and  G  are  12 
3  and  4  are     7  G  and  7  are  13 
3  and  5  are     8  6  and  8  are  14 
3  and  6  are     9  6  and  9  are  15 
3  and  7  are  10  7  and  7  are  14 
3  and  8  are  11  7  and  8  are  15 

3  and  9  are  12  7  and  9  are  16 

4  and  4  are     8  8  and  8  are  1G 
4  and  5  are     9  8  and  9  are  17 
4  and  6  are  10  9  and  9  are  18 

Let  the  above  combinations  be  repeated  also  in  the  reversed 
order  ;  thus,  2  and  5  are  7,  5  and  2  are  7.  etc. 

The  above  may  also  be  used  for  subtraction,  the  third  column 
being  the  minuend,  and  either  of  the  others  the  subtrahend. 

Copy  the  above  on  slate,  or  board,  in  each  form,  using  the  signs. 


ARITHMETIC.  89 


LESSON    LXXVIII. 
How  many  are 


2  +  22,  2  +  32,  etc.,  to  2  +  92? 
3  +  2,  3  +  12,  3  +  22,  3  +  32,  etc.,  to  3  +  92? 


8.  4  +  2,  etc.,  to  4  +  92? 

4.  5  +  2,  etc.,  to  5  +  92? 

5.  6  +  2,  etc.,  to  6  +  92? 


6.  7  +  2,  etc.,  to  7  +  92? 

7.  8  +  2,  etc.,  to  8  +  92? 

8.  9  +  2,  etc.,  to  9  +  92? 


How  many  are 
P.  2  +  3y  2  +  13,  etc.,  to  2  +  93? 

10.  3  +  3,  3  +  13,  etc.,  to  3  +  93? 

11.  The  same  also,  with  4,  5,  6,  7,  8,  and  9. 

12.  Then  2  +  4,  etc.,  3  +  4,  etc.,  4  +  4,  etc.,  as  above. 
18.  In  the  same  way,  2  +  5,  etc.,  3  +'5,  etc.,  to  9  +  5,  etc., 

till  the  sum  is  9  +  85. 

The  foregoing  is  given  only  as  a  sample  of  a  series  of  exercises, 
which  will  help  to  secure  rapidity  and  accuracy  in  all  possible  com- 
binations of  the  9  digits  with  any  number. 

1.  Name  all  the  numbers  in  combinations  of  two  each, 
that  make  4.  Ans.  3  +  1=4,  2  +  2=4,  1  +  3=4. 

2.  Name  all  that  make  5. 

Ans.  4  +  1,  3  +  2,  2  +  3,  and  1  +  4. 
8.  That  make  6.  Ans.  5  +  1,  4  +  2,  3  +  3,  2  +  4,andl  +  5. 
In  the  same  manner,  the  numbers  that  make, 

7  9        11         13        15        17        19        21        23 

8  10         12         14        16         18        20         22        24 
4.  Write  on  the  slate  or  board  a  table  of  each  ;  thus  of  7, 

6  +  1  =  7,  5  +  2  =  7,  4  +  3  =  7,  3+4=7,  2  +  5  =  7,  1  +  6  =  7. 
7-1  =  6,  7-2=5,  7-3=4,  7-4=3,  7-5=2,  7-6=1. 


90  FIRST     BOOK 

LESSON     LXXIX. 

1.  How  many  tens  in  34  units  ?   Ans.  3  tens  and  4  units. 

2.  How  many  tens  in  37  units  ?     In  56  units  ? 

3.  How  many  hundreds  in  30  tens  ?     In  50  tens  ? 

4.  How  many  hundreds  in  3G  tens  ? 

EXERCISES  FOB  THE  SLATE  A^D  BOARD. 
1.  What  is  the  sum  of  524,  315,  and  472  ? 

524  Write  units  of  the  same  order  in  the  same 

345          column. 

AH**  Begin  at  the  bottom  of  the  units  column,  and 

add  each  column  separately,  and  instead  of  say- 

Sum  1342  ing  3  units  and  5  units  are  8  units,  and  4  units 
are  12  units,  name  the  successive  results  only ; 
thus,  3,  8,  12,  the  sum  of  the  units,  equal  to  \  ten  and  2  units. 
Write  the  2  units  in  units'  place,  and  add  the  1  ten  to  the  lower 
number  in  the  tens' column  ;  then,  1,  8,  12, 14,  the  sum  of  the  tens, 
equal  to  1  hundred  and  4  tens.  Write  the  4  tens  in  tens' place  and 
add  the  1  hundred  to  the  hundreds' column ;  then,  1,  5,  8,  13,  the 
sum  of  the  hundreds,  equal  to  1  thousand  and  3  hundreds,  which 
Write  in  the  hundreds'  and  thousands'  places. 


In  the 
(2.) 
423 
542 
365 

(*.) 

134 

250 
675 

same  manner  copy, 
(8.)     (4.) 
304    210 
718    634 
532    184 

and  add  : 
(5.)     (6.) 
514     75 
301     610 
198    393 

716 
84 
205 

men. 

(9.) 
384 
92 
807 

boys. 

(10.) 
300 
480 

78 

pounds. 

(6 

(11.) 

2036 
462 

84 

days. 

ARITHMETIC. 


LESSON    LXXX, 


91 


Count 

1.  By  2's  from  0  to  36. 

9.  By  5's  from  0  to  40. 

2.  By  3's  from  0  to  27. 

10.  By  5's  from  1  to  36. 

3.  By  3's  from  2  to  29. 

11.  By  5's  from  2  to  37. 

4.  By  3's  from  1  to  31. 

12.  By  5's  from  3  to  38. 

5.  By  4's  from  0  to  40. 

13.  By  6's  from  0  to  36. 

6.  By  4's  from  1  to  37. 

14.  By  6?s  from  2  to  38. 

7.  By  4's  from  2  to  38. 

15.  By  6's  from  4  to  40. 

8.  By  4's  from  3  to  39. 

16.  By  6's  from  5  to  41. 

Count  back 

17.  By  2's  from  30  to  0. 

26.  By  5's  from  40  to  0. 

18.  By  2's  from  29  to  1. 

27.  By  5's  from  41  to  1. 

19.  By  3's  from  30  to  0. 

28.  By  5's  from  42  to  2. 

20.  By  3's  from  28  to  1. 

29.  By  5's  from  43  to  3. 

21.  By  3's  from  29  to  2, 

30.  By  6's  from  37  to  1. 

22.  By  4's  from  40  to  0. 

31.  By  6's  from  39  to  3. 

23.  By  4's  from  41  to  1. 

32.  By  6's  from  38  to  2. 

24.  By  4's  from  42  to  2. 

33.  By  6's  from  40  to  4. 

25.  By  4's  from  43  to  3. 

34.  By  6's  from  41  to  5. 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 
Copy  and  add 


3 

(*•) 

3     3 

3 

3 

(ft) 

3     3 

3 

3 

(S.) 
3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

3 

3     3 

3 

2 

1     0 

0 

4 

3     2 

1 

5 

4    3 

2 

92  FIRST     BOOK 

LESSON     LXXXI. 

1.  Count  alternately  by  2's  and  3's  to  35. 

*  Written,— 2  +  3  +  2  +  3  +  2  +  3  +  2  +  34-2  +  3  +  2  +  3  +  2  +  3. 
Counted,— 5,  7,  10,  12,  15,  17,  20,  22,  25,  27,  30,  32,  35. 
Count 


2.  By  2's  and  3's  to  40. 

3.  By  3's  and  4's  to  28. 

4.  By  2's  and  4's  to  36. 


5.  By  2's  and  5's  to  28 

6.  By  3's  and  5's  to  32, 

7.  By  4's  and  5's  to  36. 


EXERCISES  FOR  THE  SLATE  AISTD  BOARD. 
Copy  and  add 


(1.)                           (2.) 

(ft) 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

2 

1 

0 

0 

4 

4 

3 

3 

9 

8 

7 

6 

UO                   (*) 

(4) 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

3 

2 

1 

0 

5 

4 

3 

2 

8 

7 

6 

4 

(7.)                           (8.) 

w 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

1 

2 

3 

6 

3 

2 

1 

4 

7 

6 

8 

6 

*  This  exercise  may  at  first  be  written  partially  on  the  board  and 
counted  at  sight,  and  then  omitted  entirely. 


IN     ARITHMETIC.  93 

LESSON     LXXXII. 

1.  Count  by  7's,  from  0  to  49  ;   from  1  to  43  ;   from  2 
to  44 ;  from  4  to  46  ;  from  5  to  47  ;  from  6  to  48. 

2.  Count  by  8's,  fromOto48;  froml  to49;  from2  to  50; 
from  4  to  52  ;  from  5  to  53  ;  from  6  to  54 ;  from  7  to  55. 

8.  Count  by  9's,  from  0  to  54;  from  1  to  46;  from  2  to  47; 
from  4  to  49  ;  from  5  to  50  ;  from  6  to  51 ;  from  7  to  52 ; 

4.  Count  back  by  7's  from  49  to  0  ;  46  to  4 ;  43  to  1. 

5.  By  8's  from  48  to  0  ;  from  42  to  2  ;  from  47  to  7. 

6.  By  9's  from  45  to  0  ;  from  40  to  4 ;  from  41  to  5. 

EXERCISES  FOR  THE  SLATE  A:ND  BOARD. 

Copy  and  add, 

(L)  (2.)                          (3.) 

7777  7777  7777 

7777  7777  7777 

7777  7777  7777 

2100  3210  7654 


8 

0 

8 

•) 
8 

8 

8 

(5.) 
8     8 

8 

8 

(6.) 
8     8 

8 

8 

8 

8 

8 

8 

8     8 

8 

8 

8     8 

8 

8 

8 

8 

8 

8 

8     8 

8 

8 

8     8 

8 

3 

2 

1 

0 

6 

5     4 

3 

9 

8     7 

0 

9 

(7 

9 

9 

9 

9 

(*) 

9     9 

9 

9 

(9.) 
9     9 

9 

9 

9 

9 

9 

9 

9     9 

9 

9 

9     9 

9 

9 

9 

9 

9 

9 

9     9 

9 

9 

9     9 

9 

4321     8765     9876 


94  FIRST     BOOK 


LESSON    LXXXIII. 

Addition  at  Sight. 

1.  Any  two  numbers  less  than  100,  one  of  which  con- 
tains only  tens,  may  be  added  at  sight  (or  orally).     Thus, 
34  +  20=54. 

Observe,  that  3  tens  and  2  tens  are  5  tens  or  50,  and  the  4  units 
make  54. 

2.  Name  the  results  to  the  following : 


20+  8 

40  +  14 

50  +  18 

80  +  17 

30  +  12 

40  +  26 

60  +  33 

70  +  27 

30  +  16 

40  +  42 

60  +  25 

20  +  36 

30  +  20 

50  +  27 

70  +  14 

50  +  44 

34  +  40 

56  +  30 

17  +  60 

28  +  50 

ADDING  UNITS  AND  TENS  OKALLY. 
1.  What  is  the  sum  of  23  and  45  ? 

ANALYSIS. — 23  is  equal  to  2  tens  and  3  units  ;  45  is  equal  to  4 
tens  and  5  units  ;  2  tens  and  4  tens  are  6  tens  or  60,  and  3  units  and 
5  units  are  8  units  ;  60  and  8  are  68.  Hence  23  and  45  are  68. 


In  like  manner  find  the  sum  of 


2.  12  +  49. 

3.  23  +  64. 


4.  38  +  17. 

5.  51+26. 


6.  29  +  30. 

7.  48  +  34. 


8.  72  +  16. 

9.  37  +  26. 


EXERCISES  FOB  THE  SLATE  AND  BOARD. 

1.  What  is  the  sum  of  56  feet,  450  feet,  and  680  feet? 

2.  A  farmer  sold  48  bushels  of  wheat,  36  bushels  of 
corn,  27  bushels  of  rye,  and  28  bushels  of  barley ;  how 
many  bushels  of  grain  did  he  sell  in  all  ? 

8.  What  is  the  sum  of  1942  dollars,  and  685  dollars  ? 


IN     ARITHMETIC.  95 

LESSON     LXXXIV. 

Direct  the  attention  of  the  pupil  to  the  fact,  that  the 
same  figures  when  added,  always  give  the  same  unit  figure 
in  the  result.  That  is,  3  and  5  are  8  ;  3  and  25  are  28 ; 
3  and  45  are  48,  etc.  If,  in  adding  any  of  the  higher 
numbers,  he  hesitates,  refer  him  to  the  primary  sum  of 
those  numbers.  Thus,  if  the  pupil  hesitates  on  68  and  5, 
ask:  "What  unit  figure  do  8  and  5  give?"  (Am.  3.) 
Then  68  and  5  must  give  the  next  3  above  68,  that  is  73. 

The  pupil  should  be  required  to  perform  all  operations  on  the. 
slate  or  board,  without  moving  the  lips,  pronouncing  or  writing  the 
results  only. 

BLACKBOARD  DRILL. 
Place  an  example  upon  the  blackboard,  as  the  following: 


267189  ^a^  uPon  some  Pupil>  wn°  will  begin  with  the 

right  hand  column  and  say,  "  9,  17,  24,  27,  33,  42 
wilts,  equal  to  4  tens  and  2  units  ;  write  the  2  units 
918753       tinder  the  column  added,  and  add  the  4  tens  to  the 
592847       next  column.'*     The  next  pupil  will  without  any 
703928       delay  take  up  the  process,  beginning  with  the  4  tens 
564789       reserve(l,  and  say,  "4,   12,  14,  18,  23,  26,  34  tens, 
equal  to  3  hundreds  and  4  tens  ;  write  the  4  tens 
3533242       under  the  column  added  and  add  the  3  hundreds  to 
the  next  column."     So  in  quick  succession  let  each 
column  be  added  upwards,  then  downwards,  then  from  right  to 
left,  and  from  left  to  right,  until  the  whole  class  have  been  exer- 
cised upon  this  example. 

Very  young  children,  if  properly  drilled  on  preceding  lessons, 
may  easily  be  taught,  in  this  way,  to  add  long  columns  of  figures 
with  astonishing  rapidity  and  correctness. 

To  vary  the  above,  let  each  pupil  in  order  give  one  result  only, 
the  next  pupil,  immediately  pronouncing  the  following,  etc. 


96  FIRST     BOOK 

LESSON    LXXXV. 
EXERCISES  FOR  THE  SLATE  AND  BOARD. 


(f) 

men. 
542 
176 
628 

(2.)     (3.} 
feet.     days. 
820     153 

507    208 
418    759 

(4.)     (5.) 
feet.     miles. 
1450     2157 
1234    1528 

2357    1372 

(6.) 
pounds, 
1740 
2031 
1507 

473 

256    380 

1567    2143 

1423 

(7.) 

(8.) 

(9.) 

(10.)    (11.) 

(12.) 

1247 

5020 

1305 

3172    1526 

4214 

2072 

1513 

6040 

1094    5017 

2030 

4289 

3156 

3708 

7165    2157 

5327 

3070 

1208 

1159 

2082    1215 

1456 

Exercise 

the  class 

on  the 

following,  as  suggested  ir 

I  esson  LXXXIV. 

(13.) 

(^) 

(15.) 

(16.) 

(17.) 

3678 

8786 

78982 

37987 

216677 

2766 

5968 

69771 

66789 

569911 

8345 

8789 

68339 

44321 

543344 

3875 

9896 

56234 

91389 

576677 

(1ft 

(19.) 

(20.} 

(21.) 

(22.) 

32507 

23412 

35092 

275143 

1214187 

10325 

57638 

52803 

413100 

2742361 

47018 

15421 

47524 

650406 

1275142 

53106 

62732 

60832 

210350 

2020560 

61007 

54298 

11462 

132415 

1603915 

27589 

17323 

74260 

113765 

1846084 

ARITHMETIC. 


97 


LESSON     LXXXVI. 

1.  If  8  cents  be  taken  from  14  cents,  how  many  cents 
remain  ?  Ans.  6  cents. 

Since  14  is  diminished,  or  made  less,  by  subtracting  8  trom  it,  14, 
the  greater  number,  is  named  the  Minuend,  which  means  to  be 
diminished,  and  8,  the  less  number,  is  named  the  Subtrahend, 
v/iiich  means  to  be  subtracted. 

Since  6  shows  how  many  cents  remain  after  subtracting  8  cents 
from  14  cents,  it  is  named  the  Remainder,  or  the  Difference 
between  14  and  8. 

2.  What  is  the  difference  between  13  horses  and  9  horses  ? 

3.  Sixteen  men  are  how  many  more  than  8  men  ? 

4.  Five  cents  are  how  many  less  than  12  cents  ? 

5.  How  many  must  be  added  to  9  to  make  12  ? 

6.  Can  you  take  6  boys  from  11  sheep  ?     Why  not  ? 
Ans.   Only  numbers  representing  things  of  the  same 

kind  can  be  subtracted. 

7.  Harry  bought  12  peaches,   and  gave  5  of  them  to 
his  sister  ;  how  many  had  he  left  ?     12 — 6=  ? 

ANALYSIS.— He  had  left  the  difference  between  12  and  5,  which 
is  7.  12-5=7. 

8.  On  a  tree  were  1G  pigeons,  and  9  flew  away ;  how 
many  were  left  on  the  tree  ?    16 — 9~  ? 

9.  How  many  are 

19_  6?  24  less    6?  4  from  11? 

20—10?  15  less    9?  7  from  19? 

17—11  ?  21  less    7  ?  8  from  24  ? 


98  FIBSTBOOK 

LESSON     LXXXVII. 

1.  How  many  are  10  less  2  ?     11  less  2  ?    12  less  2  ? 
13  less  2  ?  etc.,  to  20  less  2  ? 

2.  How  many  are  10  less  3  ?     11  less  3  ?     12  less  3  ? 
13  less  3  ?  etc.,  to  30  less  3  ? 

3.  How  many  are  10— 4?  11—4?  12  —  4?  13—4?  etc. 

4.  Subtract  7  from  10  :  from  11 ;  from  12  ;  from  13  ;  etc. 

5.  Take  8  from  10  ;  from  11 ;  from  15  ;  from  16  ;  etc. 

6.  How  many  are  10—9  ?     11  —  9  ?     12  —  9  ?    14—9  ? 
15_9?     16-9?  etc.,  to  35-9? 

7.  George  had  17  marbles,  and  gave  five  to  one  boy  and 
4  to  another  ;  how  many  marbles  had  he  left  ?  17  —  9=  ? 

ANALYSIS.— He  liad  left  the  difference  between  the  sum  of  5  mar- 
bles and  4  marbles  or  9  marbles,  and  17  marbles  which  is 
8  marbles. 

8.  Jane  had  18  cents,  and  she  bought  a  yard  of  ribbon 
for  6  cents,  and  a  spool  of  thread  for  5  cents  ;  how  many 
cents  had  she  left  Y    18— 11=  ? 

9.  James  bought  a  ball  for  10  cents  and  a  pencil  for 
6  cents.   How  much  change  should  he  receive  for  25  cents  ? 

*  10.  Copy  and  write  the  result  in  place  of  ( ? ) : 
14—7=  ?  21—8=?  24—10=? 

18-5=  ?  19-7=?  21-9=? 

12—3=?  15—4=?  17—  8=  ? 

11.  Also  the  following  : 

6  +  10—4=?  12  +  5—8=?  14—10  +  12=? 

7__  4  +  8=?  20—9  +  12=?  25+   7—  2=  ? 

9+5_6— ?  16  —  7  +  13=?  18—9  +  20=? 


IK    ARITHMETIC. 


99 


LESSON     LXXXVIII. 

When  numbers  are  so  large  that  the  difference  cannot 
be  found  at  once,  units  may  be  taken  from  units,  tens 
from  tens,  and  hundreds  from  hundreds,  etc. 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 
1.  Subtract  644  from  968. 

Minuend,       968  =  9  liunds.  6  tens  8  units. 
Subtrahend,  644        6      "       4    "    4     " 

Difference,     324         3       "        2    "    4      " 
PROOF. — Add  the  difference  to  the  subtrahend.    If  the  work  is 
right,  the  sum  will  equal  the  minuend.     Thus,  968—644=324,  the 
difference;  and  324  +  644—968,  the  minuend. 

In  like  manner  subtract  and  prove  the  following : 


(2.)           (3.)           (4.)           (5.) 

(ft) 

Minuend,      835           769           578           274 

857 

Subtrahend,  423           634           453           121 

524 

Difference,     412 

(7.)             (8.)            (9.)            (10.) 

(11.) 

936            792            478            891 

527 

214            351            436            170 

204 

Subtract  and  prove: 

12.     623  from  944. 

19.     899 

-673. 

18.     431  from  862. 

20.     777 

-504. 

14.     354  from  798. 

21.     999 

-657. 

15.     256  from  579. 

22.     886 

—  273. 

16.     170  from  382. 

23.     709 

—  207. 

17.     322  from  694. 

24.     686 

—  475. 

18.  4206  from  9876. 

25.  8989 

-  4736, 

100  FIRST     BOOK 

LESSON     LXXXIX, 

1.  One  ten  is  how  many  more  than  1  unit  ? 

2.  One  ten  is  how  many  more  than  3  units  ? 

3.  Two  tens  are  how  many  more  than  7  units  ? 

4.  Twenty-five  are  how  many  more  than  6  ?    than  7  ? 

5.  Two  tens  and  6  units  less  8  units  are  how  many  ? 

ANALYSIS. — 2  tens  and  6  units  are  26  units,  or  1  ten  16  units ; 
and  8  units  from  1  ten  16  units  leaves  1  ten  8  units,  or  18  units. 

6.  Three  tens  5  units  less  1  ten  6  units  are  how  many  ? 
35—16—? 

ANALYSIS. — 3  tens  5  units  equal  2  tens  15  units  ;  and  1  ten  6  units 
from  2  tens  15  units  leaves  1  ten  9  units,  or  19  units. 

EXERCISES  FOE  THE  SLATE  AND  BOARD. 

1.  Subtract  27  from  84. 

i  H  84  is  8  tens  and  4  units,  27  is  2  tens  and  7 

Minuend,        $  &         units.     Since  7  units   cannot  be  subtracted 
Subtrahend    2  7          from  4  units,  increase  the  4  units  by  1  ten  or 

10  units  from  the  next  higher  order,  making 
Remainder,  57  14  units.  7  units  from  14  units  leave  7  units, 

which  write  in  units'  place.  Since  we  have 
taken  1  of  the  8  tens,  there  are  only  7  tens  left.  2  tens  from  7  tens 
leave  5  tens,  which  write  in  tens'  place.  Hence,  27  from  84  leaves 
57.  PROOF:  57  +  27=84. 

Copy,  subtract  and  prove  the  following  : 

(*•)        •(*-)         (40        (*)        (*0 

Minuend,   439     674    523     834    423 
Subtrahend,J-72     327     247     263     276 

(7.)  (8.)  (9.)  (10.)  (11.)  (12.) 
4571  5274  7345  9876  6721  2925 
2786  1548  5456  4894  3834  1673 


IK     ARITHMETIC.  101 

LESSON    XC. 

1.  A  boy  had  9  cents,  he  earned  10  more,  then  gave 

7  to  his  sister.     How  many  cents  had  he  left  ? 

2.  Five  pounds,   7  pounds,  and  4  pounds  are  how 
many  less  than  20  pounds? 

3.  Belle  had  16  pinks,  and  gaye  3  to  Mary,  and  5  to 
Anna.     How  many  had  she  left  ? 

4-  Jennie  had  25  cents,  and  bought  some  buttons  for 

8  cents,  a  pencil  for  4  cents,  and  some  thread  for  6  cents. 
How  many  cents  had  she  left  ? 

5.  JSTed  having  19  cents,  lost  4,  spent  5,  earned  3,  and 
gave  away  6.     How  many  cents  had  he  then  ? 

6.  How  many  are  5,  7,  and  4,  less  2  and  3  ? 

7.  How  many  are  10,  3,  and  6,  less  5  and  7  ? 

8.  How  many  are  15  less  7  added  to  4*and  3  ? 

9.  How  many  are  12  less  5,  added  to  10  less  3  ? 

10.  How  many  are  13  and  7,  less  6  and  9  ? 

11.  How  many  are  10,  7,  and  5,  less  9  and  3  ? 

EXERCISE  FOR  THE  SLATE  AKD  BOARD,  OR  ORALLY. 
Copy  and  write  the  proper  number  in  place  of  ( ? ) : 


12.  18  —  7  +  7  =  ? 

13.  20  +  18  -  ?  ==  25. 
U.  9  +  11  =  10  +  ? 

15.  24  —  ?  =  7  +  9. 

16.  21  -  9  +  ?  =  19. 

17.  24  +  ?  =  12  +  18. 


18.  ?  +  16  =  26  —  6. 

19.  10  +  13  =  ?  +  11. 

20.  27  —  7  =  17  +  ? 

21.  36  +  4  =  ?  +  20. 

22.  11  +  7  =  26  —  ? 

23.  23  —  5  =  ?  +  2. 


The  teacher  should  increase  the  number  of  examples  in  every 
lesson,  as  the  capacity  of  the  class  may  require,  or  the  time  allow. 


102  FIKST    ,BOOK 

LESSON    XCI. 

How  many  are 

1.  2  from  2,  2  from  12,  etc.,  to  2  from  92  ? 

2.  2  from  3,  2  from  13,  etc.,  to  2  from  93  ? 

5.  2  from  4,  2  from  14,  etc.,  to  2  from  94  ? 
£  2  from  5,  2  from  15,  etc.,  to  2  from  95  ? 

6.  2  from  6,  2  from  16,  etc.,  to  2  from  96  ? 

6.  2  from  7,  2  from  17,  etc.,  to  2  from  97  ? 

7.  2  from  8,  2  from  18,  etc.,  to  2  from  98  ? 
&  2  from  9,  2  from  19,  etc.,  to  2  from  99  ? 
9.  2  from  10,  2  from  20,  etc.,  to  2  from  90  ? 

10.  In  the  same  manner  3  from  10,  3  from  11,  3  from 
12,  and  3  from  19,  etc.,  to  3  from  99. 

11.  Also,  4  from  10,  etc.,  5  from  10,  etc.,  until  all  the 
9  digits  have  been  used  in  the  same  way. 

12.  One  ten  is  equal  to  how  many  units  ? 

13.  One  hundred  is  equal  to  how  many  tens  ? 

H.  Two  hundred  is  how  many  tens  more  than  2  tens  ? 

15.  Three  hundred  is  how  many  tens  more  than  4 
tens  ?   than  5  tens  ? 

16.  Three  hundred  is  equal  to  2  hundred  and  how  many 
tens  ?  Ans.  300=200  and  10  tens. 

17.  If  2  tens  or  20  units  he  taken  from  3  hundred,  what 
remains  ?     Ans.  300=200  and  10  tens  :  2  tens  from  200 
and  10  tens  leave   200  and  8  tens,  or  280. 

18.  Four  hundred  and  3  tens,  less  1  hundred  and  4  tens 
are  how  many  ? 

ANALYSIS. — 4  hundred  and  3  tens,(equal  3  hundred  and  13  tens) 
less  1  hundred  and  4  tens,  equal  2  hundred  and  9  tens,  or  290. 


AKITHMETIC. 


103 


LESSON    XCII. 

EXERCISES  FOR  THE  SLATE  AXD  BOARD. 
L  Subtract  279  from  800. 


Since  9  cannot  be  taken  from  0  units,  and 
since  there  are  no  tens,  we  cannot  take  1 
from  that  order.  Going  on  to  the  order  of 
hundreds,  take  1  hundred,  equal  to  10  tens 
leaving  7  hundreds  ;  of  these  1 0  tens  take  1 
ten  or  10  units,  leaving  9  tens,  and  the  minuend  800  is  equal  to  7 
hundred  9  tens  and  10  units  (700  +  90  + 10^800).  Subtract  as  before, 


7    9    10 

Minuend,  $00 
Subtrahend,  279 
Remainder,  521 


In  like  manner  copy,  subtract,  and  prove: 

2. 

267 

from     500. 

7. 

2241 

from 

7000. 

3. 

672 

from     740. 

8. 

127 

from 

4300. 

4. 

504 

from     820. 

9. 

32 

from 

1000. 

5. 

1260 

from  3005. 

10. 

3030 

from 

10200. 

*6. 

4521 

from  6206. 

11. 

237 

from 

8040. 

Find  the 

difference  between 

12. 

524 

and  376. 

17. 

907 

and 

2340. 

13. 

427 

and  806. 

18. 

89 

and 

1472. 

U. 

900 

and  679. 

19. 

1200 

and 

164. 

15. 

321 

and  450. 

,20. 

2040 

and 

320. 

16. 

784 

and  508. 

21. 

3672 

and 

1075. 

What  is  the  result 

$%. 

Of 

3416  —  2040. 

27. 

Of  12364  - 

-  1400 

$3. 

Of 

4006  -     844. 

28. 

Of 

8070 

-4105 

24. 

Of 

6400  -     640. 

29. 

Of 

7346 

-  6462 

25. 

Of 

2706  —  1371. 

30. 

Of  20371 

-  8106 

. 

26. 

Of 

7120  —    762. 

31. 

Of  16070 

-  1284. 

104  FIRST     BOOK 

LESSON    XCIII. 
Subtraction  at  Sight. 

Any  number  may  be  subtracted  from  another  at  sight, 
if  the  difference  is  not  greater  than  10.  Thus, 

1.  9—5=4;  19— 15=4;  29— 25=4;  39—35=4,  etc. 

2.  14—6  =  8;  24—16  =  8;  34—26  =  8;  44— 36  =  8,  etc, 

3.  How  many  are 

49  —  43  ?  36  —  29  ?  63  —  58  ?  92  —  84  ? 

52  —  47?  78-70?  83-76?  81-73? 

Any  number  not  greater  than  10  can  be  subtracted  at 
sight  from  any  other  number.  Thus, 

£  8— 3=5;  18— 3  =  15;  28—3=25;  38—3=35,  etc. 

5.  15  —  7=8;  25  —  7=18;  35  —  7=28;  45  — 7=38,etc. 

6.  How  many  are 

27-8?         49-3?          51-4?         81-5?          61-2? 
36  —  7?          64—9?          73  —  6?          94-8?          75^-9? 

ORAL  AND  WRITTEN  EXERCISE. 

(^.)  Write  the  two  numbers  344  and  579,  and  add  them 

344      without  drawing  a  line,  and  write  their  sum  923  as  the 

g  w  Q      third  number ;   then  add  the  three  numbers  and  write 

their  sum,  1846,  as  the  fourth  number  ;  then  add  the  four 

numbers,  and  write  their  sum,  3692,  as  the  fifth,  and  so  on. 

The  same  example  may  be  used  for  exercise  in  sub- 

3692      traction,  by  subtracting  from  the  last  result  each  of  the 

7384      preceding  numbers  in  succession,  until  nothing  remains. 

In  the  same  manner,  copy,  add,  and  prove  the  follow- 
ing, extending  each  to  the  sixth  number  : 

(*•)     (*•)     (-*•)     (5.)     (&) 
327     674     384     540     1257 
918     241     609     703      720 


IK     ARITHMETIC. 


105 


Ml         'LICATION 


LESSON    XCIV. 

1.  If  5  boys  can  sit  upon  one  bench,  how  many  boys 
can  sit  upon  3  benches ?     5  and  5  and  5  are  how  many? 

2.  If  a  man  earn  3  dollars  a  day,  how  many  dollars  will 
he  earn  in  5  days?     3  +  3  +  3  +  3  +  3,   are  how  many? 
Five  3's,  or  5  times  3,  are  how  many  ? 

8.  Count  to  15  by  3's.     By  5's.     How  many  3's  in  15  ? 
How  many  5's  ? 

4.  There  are  7  days  in  1  week ;  how  many  days  are 
there  in  4  weeks  ?     7  +  7  +  7  +  7=?     Four  7's,  or  7  x  4=  ? 

5.  Count  by  4's  to  28.     By  7's.     How  many  4's  in  28  ? 
How  many  7's  ? 

6.  Is  the  result  of  4  times  7  and  of  7  times  4  the  same  ? 

7.  At  4  dollars  a  barrel,  what  will  6  barrels  of  apples 
cost  ?     Six  4's,  or  6  times  4,  are  how  many  ? 

8.  What  is  the  difference  between  six  3's  and  three  6's  ? 

9.  How  many  are  eight  3's  ?     3  times  8  ?     8x3? 

10.  Eepeat  the  table  from  0  times  2  to  12  times  2.  Thus, 
0  times  2  is  0,  once  2  is  2,  twice  2  are  4,  3  times  2  are  6,  etc. 

11.  Repeat  back  from  12  times  2  to  0  times  2.     Thus, 
12  times  2  are  24,  11  times  2  are  22,  10  times  2  are  20,  etc 

12.  From  0  times  3  to  12  times  3,  and  back  to  0  times  3. 

13.  From  0  times  3  to  12  times  4,  and  back. 

14.  From  0  times  5  to  12  times  5,  and  back. 


106  FIESTBOOK 

LESSON    XCV. 

1.  If  one  hat  cost  7  dollars,  what  will  4  hats  cost?  ' 

SOLUTION.— Since  1  hat  costs  7  dollars,  4  hats  will  cost  4  times  7 
dollars,  or  28  dollars. 

2.  At  6  cents  each,  what- will  5  pencils  cost? 

3.  At  8  cents  a  pound,  what  will  6  pounds  of  soap  cost  ? 

4.  If  a  man  earn  4  dollars  a  day,  how  many  dollars  can 
he  earn  in  8  days  ? 

5.  If  5  boys  have  7  marbles  each,  how  many  marbles 
have  they  all  ? 

6.  What  is  the  cost  of  6  books,  at  4  dollars  each  ? 

7.  If  a  boy  receives  5  merit  marks  a  day  for  5  days,  how 
many  marks  does  he  receive  in  all  ? 

8.  If  a  horse  troo  8  miles  an  hour,  how  far  will  he  trot 
in  6  hours  ? 

9.  Bessie  had  3  rose-bushes,  and  there  were  9  roses  on 
each  bush.     How  many  roses  upon  all  ? 

Eepeat  the  table 

10.  From  0  times  6  to  12  times  6,  and  back  to  0  times  6. 

11.  From  0  times  7  to  12  times  7,  and  back. 

12.  From  0  times  8  to  12  times  8,  and  back. 

13.  How  many  units  are  4  times  9  units  ?    How  many 
tens  ?  Ans.  3  tens  and  6  units. 

14.  How  many  are  5  times  12  units  ?    How  many  tens  ? 

15.  How  many  tens  are  6  times  5  tens  ?     How  many 
hundreds  ?     How  many  units  ? 

16.  How  many  are  4  times  6  tens  ?    How  many  hun- 
dreds and  tens  ?     How  many  units  ? 

17.  How  many  hundreds  are  3  times  7  tens  ? 


IN     ARITHMETIC.  107 


LESSON     XCVI. 

1.  Taking  one  of  two  numbers  as  many  times  as  there  are  units 
in  the  other  is  called  Multiplication. 

2.  The  number  taken  or  multiplied  is  named  the  Multiplicand. 

3.  The  number  to  multiply  by,  or  that  shows  how  many  times  the 
multiplicand  is  to  be  taken,  is  named  the  Multiplier. 

4.  The   result   obtained  by   the    multiplication    is    named    the 
Product. 

5.  The  multiplicand  and  multiplier  are  Factors  of  the  product 

6.  Thus,  8x6  =  48.    8  is  the  multiplicand,  6  is  the  multiplier,  48 
is  the  product,  and  8  and  6  are  the  factors. 


EXEECISES   FOB   THE   SLATE   AKD   BOAED. 

1.  How  many  are  3  times  42  ? 

BY  ADDITION.  BY  MULTIPLICATION.       The  result  may  be 

_   .  .         ,,,«.„          Multiplicand,    4  2      otoined  by  ^Uion. 
Numbers  Write  42  three  times 

to  be      \      42         Multipher,  3      andadd;  thesis  126. 


added,  Product,     12  6         But  it  may  be  done 

Bum,      126  much      shorter     and 

easier  by  writing  the 

multiplicand  42  but  once  ;  and  as  it  is  to  be  taken  3  times,  write 
the  multiplier  3  under  it  in  units'  place   and  multiply.      Thus, 

3  times  2  units  are  6  units,  which  write  in  units'  place  ;  and  3  times 

4  tens  are  12  tens,  or  1  hundred  and  2  tens,  which  write  in  tens' 
and  hundreds'  place.     Hence  the  product  126  is  the  same  as  the  sum, 

In  like  manner  solve  by  both  methods  : 


2.  3  times  53. 

3.  5  times  61. 

4.  4  times  220. 

5.  2  times  643. 


6.  3  times  4032. 

7.  6  times  610. 

8.  4  times  3102. 

9.  2  times  7234. 


108  FIRST     BOOK 

• 

LESSON    XCVII. 

1.  At  5  dollars  a  cord,  what  will  6  cords  of  wood  cost  ? 
7  cords  ?    8  cords  ? 

2.  If  there  are  8  trees  in  ooe  row,  how  many  trees  in 
5  rows  ?     In  8  rows  ?     In  9  rows  ?     In  10  rows  ? 

3.  If  you  earn  12  cents  an  hour,  how  many  cents  can 
you  earn  in  3  hours  ?     In  5  hours  ?     In  6  hours  ?     In  7 
hours  ?     In  10  hours  ? 

4.  How  many  are  5  times  10  cents,  and  8  cents  more  ? 

5.  How  many  are  G  times  7  dollars,  less  5  dollars  ? 

6.  James  gave  4  cents  apiece  for  5  oranges,  and  had 
10  cents  left.     How  much  money  had  he  at  first  ? 

7.  Belle  paid  G  cents  a  yard  for  3  yards  of  ribbon.     How 
much  change  should  she  receive  for  25  cents  ? 

EXERCISES  FOR  SLATE  AKD  BOARD. 
1.  How  many  are  4  times  48  ? 

Multiplicand,    4  8          The  result  may  be  obtained  by  addition,  but 
Multiplier,  4      tne  shorter  method  is  to  write  the  multiplier 

under  the  multiplicand  in  units'   place  and 
Product,     192  u.  ,       ,T 

multiply  ;  thus, 

4  times  8  units  are  32  units,  or  3  tens  and  2  units.  Write  the  2 
units  in  units'  place,  and  reserve  the  3  tens  to  add  to  the  product  of 
the  tens.  Next,  4  times  4  tens  are  16  tens,  and  the  3  tens  reserved 
added  make  19  tens,  or  1  hundred  and  9  tens,  which  write  in  hun- 
dreds' and  tens'  places.  Hence,  4  times  48  are  192. 

(2.)  (A)  (4.)  (5.) 

Multiply        72  136  247  1265 

By  _4  _j>  _3  _J> 

6.  Multiply  2436  hy  3  ;  by  5  ;  by  4  ;  by  6. 

7.  Multiply  3057  by  2  ;  by  3  ;  by  4  ;  by  5  ;  by  6. 


INAEITHMETIC.  109 


LESSON    XCVIII. 

The  following  table  contains  all  the  products  from  12  to  144  in- 
clusive that  can  be  produced  by  any  two  factors,  not  less  than  2 
nor  greater  than  12. 

These  combinations  should  be  thoroughly  committed,  and  re- 
peated in  the  reverse,  as  well  as  in  the  direct  order. 


2x    6  =  12) 

4x   8=32 

7x   9=  63 

V 

3x   4=12  \ 

3x11=33 

8x   8=  64 

2x   7=14 

5x   7=35 

6x11=  66 

3x   5  =  15 

3  x  12=36  \ 

7x10=  70 

2x   8=16) 

4x   9=36  V 

8x   9=  72 

4x   4=16) 

6x    6=36  ) 

6x12=  72 

2x   9  =  18) 

4x10=40) 

7x11=  77 

>• 

(• 

3x   6  =  18  \ 

5x   8=40  ) 

8x10=  80 

2x10=20) 

6x    7=42 

9x    9=  81 

4x   5=20) 

4x11=44 

7x12=  84 

3x   7=21 

5x    9=45 

8x11=  88 

2x11=22 

4x12=48) 

9x10=  90 

2x12=24  \ 

6x    8=48  ) 

8x12=  96 

3x   8=24  V 

7x    7=49 

9x11=  99 

4x   6=24) 

5x10=50 

10x10=100 

5x   5=25 

6x   9=54 

10x11=110 

3x   9=27 

5x11=55 

10x12=120 

4x   7=28 

7x   8=56 

11x11  =  121 

3x10=30) 

6x10  =  60) 

11x12=132 

5x   6=30  ) 

5x12  =  60  ) 

12x12=144 

The  above  may  also  be  used  as  a  division  table,  the  numbers  in 
the  third  column  being  used  as  dividends,  and  those  either  in  the 
first  or  second  as  divisors.  Thus,  2  times  6  are  12  ;  6  times  2  are 
12.  6  in  12,  2  times  ;  2  in  12,  6  times,  £  of  12  is  6  ;  -J-  of  12  is  2. 


110  FIKST     BOOK 

LESSON    XCIX. 

The  following  are  all  the  products  in  the  multiplica- 
tion table  to  132. 

Let  the  pupil  at  sight,  or  upon  hearing  a  number,  name  at  least 
one  set  of  factors.  Thus,  21.  Am.  7  times  3,  or  3  times  7.  60. 
Ans.  6  times  10,  or  5  times  12,  etc. 


4 

20 

35 

55 

81 

6 

21 

36 

56 

88 

8 

22 

40 

60 

90 

9 

24 

42 

63 

96 

1G 

25 

44 

64 

99 

12 

27 

45 

66 

100 

14 

28 

48 

70 

108 

15 

30 

49   ' 

72 

110 

16 

32 

50 

77 

121 

18 

33 

54 

80 

132 

EXERCISES  FOR  THE  SLATE  AXD  BOARD. 

(1.)  (2.)  (3.)  (4.) 

1026  4150  6703  14037 

_8  _6  _5_  4 

5.  If  there  are  52  weeks  in  1  year,  how  many  weeks 
are  there  in  8  years  ? 

6.  If  a  steamer  run  265  miles  a  day,  how  many  miles 
will  she  run  in  7  days  ? 

7.  A  man  bought  4  houses,  and  paid  4385  dollars  for 
each.     What  did  he  pay  for  all  ? 

8.  In  1  mile  are  5280  feet.     How  many  feet  in  3  miles  ? 


ARITHMETIC. 


Ill 


LESSON    C. 

EXERCISES  FOR  SLATE  AND  BOARD,  OR  ORALLY. 
Give  the  result  of 


3x7 

5x3 

6x3 

9x7 

6x  7 

7x5 

8x8 

9x9 

4x6 

8x  3 

4x9 

7x6 

8x7 

5x8 

3x  9 

9x6 

4x7 

6x9 

7x5 

3x10 

The  pupil  may  make  oral  problems  for  the  above.  Thus,  for 
"3x7."  "  What  will  7  lemons  cost  at  3  cents  each?"  Another 
pupil  may  solve  the  same  by  a  simple  analysis ;  thus,  7  lemons 
will  cost  7  times  3  cents,  or  21  cents. 

Copy,  and  write  the  result  in  place  of  (?): 


8x7+  4=? 
7x9  +  10=  ? 
6x6+  8=? 
4x4+  9=  ? 

9x8-12=? 
8x6-  9=? 
9x9—10=  ? 
10x8-  7=? 

7x  9  +  10=? 
8x11—  8=  ? 
7x10  +  12=? 
11  x  6-  9=? 

FOR  THE  SLATE  AND  BOARD. 

In  the  following,  the  numbers  given  as  multiplicands  may  each 
be  multiplied,  separately,  by  each  of  the  multipliers  following  it  ; 
or  first  by  one  of  them  and  the  product  by  the  next,  and  so  on. 


1.  9704x2,  4,  6,  8. 

2.  658x3,  5,  7,  6. 

3.  1463x4,  2,  3,  5. 

4.  2789x3,  4,  2,  6. 

5.  3596x2,  4,  3,  5. 

6.  2043x4,  5,  2,  7. 


7. 
8. 
9. 
10. 
11. 
12. 

3804  x  5,- 
2964  x  3, 
4070  x  5, 
5164  x  7, 
3005  x  8, 
10804  x  6, 

6, 
8, 
9, 
8, 
9, 
7, 

7. 
6. 
4. 
9. 
5. 
8,  9. 

8x12=? 

6x?=72           ?  x7 

9x 

6==? 

?> 

;5=r45 

12  x? 

12 

p 

12 

p 

7 

12 

8 

8 

p 

9 

p 

p 

T 

96 

96 

72 

63 

84 

112  FIRST     BOOK 

LESSON    CI. 
Multiplication  at  Sight. 

14         9x  ?  =81 
iO          ?xll  =  77 

?          ?  11 

_9        12  J> 

81         60  99 
This  exercise  may  be  continued  at  the  option  of  the  teacher. 

EXERCISES  FOR  THE  SLATE  A:NTD  BOARD. 
1.  Multiply  362  by  24. 

Multiplicand,  362  Write  the  multiplicand,  and 

Multiplier,  24  under  U  the    multiplier,    the 

units  in  units'  place,  and  the 
4  times,      tens  in  tens'  place,  and  multi- 
724          20  times.   .  ply  by  each  figure  separately. 

Multiply  362  by  the  4  units, 
Product,        o  o  o  o       /e  4  times. 

and  tlien   by  the  ~  tens  ;  add 

the  products,  and  the  sum  is  the  entire  product,  8688. 

In  multiplying  by  the  units,  write  the  first  figure  of  the  product 
in  units'  place.  In  multiplying  by  the  tens,  write  the  first  figure 
of  the  product  in  tens'  place. 

In  the  same  manner,  multiply 


2.  487  by  18. 

3.  618  by  23. 


4.  3241  by  16.         6.  894  by  22. 

5.  2046  by  25.          7.  709  by  36. 


8.  Multiply  30426  by  17  ;  by  28  ;  by  35  ;  by  44 ;  by  42. 

9.  Multiply  24305  by  52  ;  by  48  ;  by  65  ;  by  72  ;  by  66. 
10.  Multiply  426173  by  61;  by  43;  by  53;  by  19;  by  34. 

The  teacher  should  increase  these  examples  according  to  the 
wants  and  capacity  of  the  class  ;  also  instruct  them  how  to  multi- 
ply by  10,  or  100. 


ARITHMETIC. 


113 


DTVISIOIV 


LESSON    GIL 

1.  How  many  times  3  peaches  are  18  peaches  ?    How 
many  3's  in  18  ?     18-7-3=  ? 

2.  How  many  times  can  4  oranges  be  taken  from  16 
oranges?    How  many  4's  in  16  ?     16-7-4=  ? 

3.  How  many  times  4  pounds. are  20  pounds?    How 
many  4's  in  20  ? 

4.  How  many  times  can  4  be  taken  from  20  ?    4  in  20 
how  many  times  ?     20-7-4=  ? 

5.  If  a  box  will  hold  5  pounds  of  honey,  how  many 
such  boxes  will  hold  30  pounds  ? 

6.  How  many  times  5  pounds  are  30  pounds  ?     How 
many  5's  in  30  ?   How  many  times  can  5  be  taken  from  30  ? 

7.  From  a  pile  of  24  marbles,  how  many  groups  of  4 
marbles  each  can  be  made  ?    4  in  24,  how  many  times  ? 

8.  How  many  groups  of  6  each  ?    How  many  6's  in  24  ? 

9.  How  many  groups  of  3  each  ?    How  many  3's  in  24  ? 

10.  How  many  groups  of  8  each  ?    How  many  8's  in  24  ? 

11.  How  many  groups  of  2  each  ?    How  many  2?s  in  24  ? 

12.  How  many  times  can  8  dollars  be  taken  from  24 
dollars  ?     From  40  dollars  ?    From  56  dollars  ? 

13.  How  many  times  8  in  24  ?   In  40  ?   In  56  ?  In  64  ? 

14.  How  many  times  9  boys  cfre  27  boys  ?    Are  36  boys  ? 

15.  How  many  9's  in  18  ?  In  27  ?  In  54  ?  In  72  ?  In  81  ? 


FIEST     BOOK 

LESSON    CIII. 

1.  At  4  cents  each,  how  many  lemons  can  be  bought 
for  20  cents  ? 

SOLUTION.  —As  many  lemons  can  be  bought  for  20  cents,  as  4 
cents  are  contained  times  in  20  cents,  which  are  5  times.  Hence,  at 
4  cents  each  5  lemons  can  be  bought  for  20  cents. 

2.  If  a  man  earn  3  dollars  a  day,  in  how  many  days 
can  he  earn  12  dollars?  18  dollars?  27  dollars?  30  dollars? 

3.  If  a  horse  travel  7  miles  an  hour,  in  how  many  hours 
can  he  travel  28  miles  ?    42  miles  ?    63  miles  ?   70  miles  ? 

4.  If  5  lemons  cost  20  cents,  what  is  the  price  of  each  ? 

SOLUTION. — Since  5  lemons  cost  20  cents,  1  lemon  will  cost  1  -fifth 
of  20  cents,  or  4  cents. 

5.  Do  you  find  how  many  times  5  lemons  are  contained 
in  20  cents,  or  do  you  find  one  of  5  equal  parls  of  20  cents  ? 

6.'  How  do  you  find  one  of  5  equal  parts  of  a  number  ? 
One  of  4  equal  parts  ?  One  of  7  equal  parts  ? 

7.  How  many  times  5  miles  are  40  miles  ? 

8.  What  is  1  of  5  equal  parts,  or  1  fifth  of  40  miles  ? 

9.  If  18  boys  sit  on  3  benches,  how  many  boys  sit  on 
each  bench  ?     1  third  of  18  boys  are  how  many  boys  ? 

10.  If  6  tons  of  coal  cost  3G  dollars,  what  is  the  cost 
of  1  ton  ? 

11.  If  8  cords  of  wood  cost  40  dollars,  what  is  the  cost 
of  1  cord  ? 

The  teacher  will  observe  and  illustrate  that  both  forms  of  divi- 
sion are  deductions  from  multiplication.  Thus,  since  8  times  4  are 
12,  it  follows  that  4  is  in  13  three  times,  and  that  1  third  of 
12  is  4. 


IN     ARITHMETIC. 


115 


LESSON    CIV. 

1.  Finding  how  many  times  one  number  is  contained  in  another 
of  the  same  kind,    or  finding  one  of  the  equal  'parts  of  a  number,  is 
called  Division. 

2.  The  number  divided  is  named  the  Dividend. 

3.  The  number  used  to  divide  by  is  named  the  Divisor. 

4.  The  result  obtained  by  the  division  is  named  the  Quotient. 

5.  The  divisor  and  quotient  are  the  factors  of  the  dividend. 

6.  When  the  division  is  not  exact,  the  part  of  the  dividend  re- 
maining is  called  the  Remainder,  and  it  must  always  be  less 
than  the  divisor. 

7.  Thus,  in  the  example,  72  -s-  8  =  9,  72  is  the  dividend,  8  is  the 
divisor,  and  9  is  the  quotient.    PROOF  :  8  x  9  —  72. 


EXEECISES   FOR   SLATE  ASTD   BOARD. 

1.  Divide  4680  by  2. 


Divisor,  Dividend.         Write  the  divisor  at  the  left  of  the  dividend, 
2     )     4680       with  a  curved  line  between  them,  and  draw  a 
~~^~     line  under  the  dividend.      Begin  with    the 
highest  order  and  divide,  thus:  2  in 4,  2  times  ; 


Quotient,  23 


2  in  6,  3  times ;  2  in  8,  4  times  ;  2  in  0,  0  times,  writing  each  quo- 
tient figure  under  the  figure  divided,  since  it  is  the  same  order  of 
units  as  that  figure.  PROOF:  2340  x  2  =  4680. 

In  the  same  manner,  divide  and  prove 


2.  396  by  3. 
8.  8088  by  8. 
4.  5050  by  5. 
5.  4884  by  4. 
6.  7007  by  7. 

7.  8462  by  2. 
8.  6248  by  3. 
9.  9603  by  3. 
10.  8008  by  8. 

11.  7777  by  7. 

12.  8408  by  4. 
18.  5550  by  5. 
14.  7007  by  7. 
15.  8642  by  2. 
16.  9000  by  9. 

116 


FIRST     BOOK 


LESSON    CV. 

EXERCISES  ox  THE  TABLES. 

1.  Divide  and  prove  ;  thus,  2  in  16,  eight  times  ;  8  times 
2  are  16. 


18-5-6 
27-5-9 
28-5-4. 


28-7-7 
36-7-6 

42-5-7 


36  —  9 
45  —  5 

48-6 


40-^8 
66-7-7 

54-5-9 


In  proving  division,  multiply  the  divisor  by  the  quotient,  not  the 
quotient  by  the  divisor. 

2.  In  ,the  same  manner,  give  the  quotient  and  proof  of 
the  following  : 

64  —  8=         '77  —  11=          81—9=          84  —  7  = 
72  —  9=  56—8=          72—8=          80-8  = 

63  —  7  =  70  —  10  =          60  —  12  =          63  —  9  = 

3.  In  the  following,  find  the  product,  and  then  each 
factor,  thus: 

Given  8x4.     4  times  8  are  32 ;  8  in  32,  four  times  ; 
1  fourth  of  32  is  8. 

12  x    3 

9x6 
8  x  11 
9x9 

4.  Copy  and  write  the  correct  number  in  place  of  ( ? ) : 
Quotients,  7          ?          ?         8         9         6         ? 
Divisors,             _?       __7       J      _?      _9       _?       _5 
Dividends           70       70       63       64         ?       54       60 


6x7 

9x5 

9x8 

7x5' 

8  x  7 

7  x  9 

8x6 

6x9 

10  x  7 

7x6 

9x4 

8  x  10 

ARITHMETIC. 


117 


LESSON    CVI. 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 


1.  Divide  447  by  3. 

Divisor.  Dividend.  Quotient. 
3  )    447   (  149 
3_ 
14 
12 

27 

2_7 

0 


In  this  example,  write  the  divisor 
at  tiie  left,  and  the  quotient  at  the 
right  of  the  dividend,  and  begin  at 
the  left  to  divide,  thus :  8  is  contained 
in  4, 1  time  and  a  remainder  ;  write  1 
for  the  first  figure  of  the  quotient  and 
multiply  the  divisor  3  by  it,  and  sub- 
tract the  product  3  from  4  hundreds, 
the  number  divided,  and  the  Remainder 
is  1  hundred,  equal  to  10  tens,  to  which 
add  the  4  tens  of  the  dividend,  making 
14  tens,  expressed  by  bringing  down  the  4  to  the  right  of  the  1  hun- 
dred. Then  3  is  contained  in  14,  4  times  and  a  remainder.  Write 
the  4  in  the  quotient,  multiply  the  divisor  by  it,  and  subtract  the 
product  12  from  14,  and  the  remainder  is  2  tens,  or  20  units,  to 
which  add  the  7  units  of  the  dividend,  making  27.  3  is  contained 
in  27,  9  times.  Multiplying  and  subtracting  as  before,  nothing 
remains.  PROOF  :  149  x  3  =  447. 

The  work  may  be  shortened  very  much  by  what  is  termed  Short 
Division,  as  follows : 

3  is  contained  in  4,  1  time  and  1  remainder ;  1  pre- 
3  )  447       fixed  or  placed  before  4,  makes  14 ;  3  in  14,  4  times 
-^  4  g       and  2  remainder  ;  2  prefixed  to  7  makes  27  ;  3  in  27, 
9  times.     Hence  the  quotient  is  149. 

In  like  manner,  divide  and  prove 


2.  8752  by  4. 
S.  7625  by  5. 
4.  7122  by  6. 

5.  5343  by  3. 
6.  8561  by  7. 
7.  9024  by  8. 

8.  76344  by  6. 
9.  90324  by  4. 
10.  83210  by  5. 

118  FIRST     BOOK 

LESSON    CVII. 

1.  If  6  men  earn  24  dollars,  what  part  of  24  dollars 
does  1  man  earn  ?     How  many  dollars  ? 

2.  At  9  cents  a  quart,  how  many  quarts  of  milk  can  be 
bought  for  63  cents  ? 

3.  How  do  the  solutions  of  these  two  examples  differ  ? 

4.  When  the  divisor  and  dividend  are  of  the  same  name 
or  kind,  what  do  we  do  ?    Ans.  Find  how  many  times  the 
dividend  contains  the  divisor. 

5.  What  is  the  quotient  ?  Ans.   Times. 

6.  When  the  divisor  and  dividend  are  not  of  the  same 
name  or  kind,  v/hat  do  we  do  ? 

Ans.  Find  a  certain  part  of  the  dividend. 

7.  What  is  the  quotient?    Ans.  A  part  of  the  dividend 

8.  How  many  yards  of  cloth,  at  7  dollars  a  yard,  can  be 
bought  for  70  dollars  ?    For  63  dollars  ?    For  84  dollars  ? 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 

1.  How  many  times  is  6  contained  in  1834? 
Divisor.  Dividend.  Since  6  is  not  contained  in  1,  say,  6  in 

6)1834         18,  3  times  and  no  remainder  ;  6  in  3,  0  times 

"  '•  6  in  34' 


Quotiento54  •  '       mes  an       re' 

mamder,  which  write  over  the  divisor  6,  as  a 

part  of  the  quotient.     PROOF  :  305  x  6  +  4  =  1834. 
In  like  manner, 

2.  Divide  3324  by  2  ;  by  4  ;  by  6  ;  by  7  ;  by  8. 
8.  Divide  9106  by  3  ;  by  4  ;  by  5  ;  by  8. 

4.  Divide  60530  by  5  ;  by  6  ;  by  7  ;  by  8  ;  by  9. 

5.  Divide  65625  by  3  ;  by  4  ;  by  7  ;  by  8  ;  by  9. 


IK     ARITHMETIC.  119 

LESSON    CVIII. 

AKOTHER  FOKM   OF   EXPKESSISTG   DIVISION". 

1.  Division  is  sometimes  indicated  by  placing  the  divi- 
sor "under  the  dividend,  and  separating  them  by  a  line. 

Thus,  if  means  12  divided  by  4,  or  1  fourth  of  12,  and  is  the  same 
as  12-7-4,  the  quotient  being  3. 

2.  Find  the  quotient,  or  value,  of  each  of  the  following: 

V;      V;      ¥;      ¥;      ¥;      ¥;      -¥-; 
¥;      «;      V;      ¥;      ¥;      ¥;      ¥• 

This  form  of  indicating  division  often  simplifies  two  or  more 
operations  that  are  to  be  performed ;  thus, 

3.  It  is  required  to  multiply  12  by  5,  and  divide  the 
product  by  6. 

Written,  ^—=10  ;  for,  12  x  5  =  60,  and  1  sixth  of  60, 

or  60  -f-  6  ^  10. 

4.  To  7  times  8  add  4  and  divide  the  sum  by  6. 

8  v  74-4 
Written,  -  ^r1—  =  10  ;  for,  8  x  7  is  56,  plus  4  is  60, 

and  1  sixth  of  60,  or  60  ~  6  =  10. 

Express  by  signs  each  of  the  following  : 

5.  Divide  the  difference  between  17  and  5  by  4. 

6.  Divide  the  product  of  12  and  4  by  8. 

7.  What  is  1  seventh  of  the  sum  of  34  and  8  ? 

8.  From  the  sum  of  25  and  10  subtract  5,  and  divide 
the  remainder  by  6. 

9.  From  the  product  of  10  and  7  subtract  6,  and  divide 
the  remainder  by  8. 


120  FIRST     BOOK 

LESSON    CIX. 

1.  What  is  1  half  of  12  ?     Of  16  ?     Of  18  +  G  ? 

2.  What  is  1  third  of  15  ?     Of  18  ?     Of  21  +  9  ? 
8.  What  is  1  fourth  of  1 6  ?     Of  24  ?     Of  30  +  6  ? 

4.  What  is  1  fifth  of  20  ?     Of  30  ?     Of  40  -  5  ? 

5.  What  is  1  sixth  of  24  ?     Of  36  ?     Of  38  +  10  ? 

6.  What  is  1  seventh  of  35  ?     Of  42  ?     Of  60  —  11  r 

7.  What  is  1  eighth  of  48  ?     Of  32  ?     Of  70  —  6  ? 

8.  What  is  1  ninth  of  54  ?     Of  63  ?     Of  60  +  12  ? 

9.  What  is  1  tenth  of  90  ?     Of  87  —  7  ?     Of  62  +  8  ?* 

10.  What  is  £  of  4  times  9  ?    J  of  5  times  8  ? 

11.  What  is  \  of  60  —  4?    $  of  12  x  4  ?    |  of  66  +  6  f 
m  What  is  t  of  6x6?    £  of  12x6?    £  of  75  -  9  ? 

EXERCISES  FOR  THE-  SLATE  AND  BOARD. 
Find  the  value  of  each  of  the  follomng  expressions  in 
a  single  number  : 


('.) 

21  —  9 

(*•) 

43-7 

(*) 

12  x  5 

(*) 

9x8 

6 

6 
(5.) 

7x9  +  7 

9 
8x9-8 

10 

(*•) 

6  x  9  +  10 

12 
12  x  7  + 

7 
(ft) 

13  +  34 

8 

( 
42  + 

8 
36  —  14             45 

9 

(1L) 

x  4  +  4 

12 


128  x  3  28  x  16  242  x  21 

4  8  7 


IK     AEITHMETIC.  121 

LESSON    CX. 

1.  If  4  caps  cost  12  dollars,  what  will  6  caps  cost  ? 

SOLUTION. — Since  4  caps  cost  12  dollars,  1  cap  costs  1  fourth  of 
12  dollars,  or  3  dollars  ;  and  6  caps  will  cost  6  times  3  dollars,  or 
18  dollars. 

2.  How  many  dollars  are  6  times  1  fourth  of  12  dollars  ? 

3.  If  6  oranges  cost  18  cents,  what  will  8  oranges  cost? 

4.  If  7  yards  of  ribbon  cost  56  cents,  what  will  3  yards 
cost  ?     5  yards  ?     8  yards  ?     6  yards  ?     9  yards  ? 

5.  If  a  man  earn  30  dollars  in  6  days,  how  many  dol- 
lars does  he  earn  in  4  days  ?     In  3  days  ?    In  5  days  ? 

6.  How  many  yards  of  cloth  can  I  buy  for  36  dollars, 
if  3  yards  cost  12  dollars  ? 

7.  If  a  man  walk  27  miles  in  9  hours,  how  far  does  he 
walk  in  7  hours  ? 

8.  How  many  are  8  times  %  of  42  ?     9  times  £  of  35  ? 
10  times  |  of  18  ?     6  times  %  of  72  ? 

EXERCISES  FOE  THE  SLATE  AKD  BOARD. 

1.  If  6  acres  of  land  are  worth  366  dollars,  what  are 
8  acres  worth  ? 

2.  If  there  are  174  lines  on  6  pages  of  this  book,  how 
many  lines  on  1 6  pages  ? 

3.  If  8  cords  of  wood  are  worth  32  dollars,  what  are 
27  cords  worth  ? 

4.  What  will  45  pounds  of  beef  cost,  if  8  pounds  cost 
96  cents  ? 

5.  If  10  tons  of  coal  are  worth  70  dollars,  what  are 
125  tons  worth  ? 


122  FIESTBOOK 

LESSON    CXI. 

EXERCISES  FOE  THE  SLATE  AND  BOARD. 

1.  Divide  3180  by  15. 

15)3180(212  When  the  divisor  consists  of  two  or  more 

3  Q  figures,  the  operations  of  multiplying  and 

subtracting  cannot  well  be  carried  on  in  the 

mind,  and  so  we  write  the  result  of  each 

1  5  separate  operation. 

o  r\  Since  15  is  not  contained  in  3,  we  say  15 

in  31,  2  times,  and  write  the  2  at  the  right 
U  of  the  dividend  as  the  first  figure  of  the  quo- 

tient.    Multiply  the  divisor  by  this  quotient 
figure,  and  write  the  product  30  under  the  figures  divided. 

Subtract,  and  to  the  remainder  1,  annex  8,  the  next  figure  of  the 
dividend,  making  18  for  a  new  dividend. 

Dividing,  multiplying  and  subtracting  as  before,  we  have  a 
remainder  of  3,  to  which  annex  the  0  of  the  dividend,  and  we  have 
a  new  dividend  of  30  ;  which  divide  as  before,  and  nothing  re- 
mains. PROOF  :  212  x  15=3180. 

2.  Divide  12708  by  28. 

Divisor.  Dividend.  Quotient.  PROOF. 

28)12708(453f|  453  Quotient. 

112  28  Divisor. 

150  3624 

140  906 

108  12684 

84  24  Remainder. 

2  4  Remainder.  12708  Dividend. 

If  the  product  of  the  divisor  by  the  quotient  figure  is  greater 
than  the  part  of  the  dividend  divided,  the  quotient  figure  is  too 
great  and  must  be  diminished.  If  the  remainder  after  any  subtrac- 
tion is  greater  than  the  divisor,  the  quotient  figure  is  too  small, 
and  must  be  increased. 


IN     ARITHMETIC.  123 

LESSON    CXII, 

1.  How  many  times  is  5  contained  in  10  x  6  ? 

2.  How  many  times  is  3  x  3  contained  in  G3  ? 

8.  Divide  48  by  1  sixth  of  24.     By  1  fourth  of  32. 

4.  A  boy  gave  5  peaches  to  each  of  6  boys,  and  had 
1  third  as  many  left.     How  many  had  he  left  ? 
•    5.  Mary  has  5  cents  and  Susie  7.     If  Willie  has  4  times 
as  many  as  both,  how  many  cents  has  he  ? 

6.  What  is  1  fourth  of  6  times  8  ?  1  third  of  5  times  6  ? 

7.  A  man  sold  8  barrels  of  apples  at  5  dollars  a  barrel. 
How  many  yards  of  cloth,  at  4  dollars  a  yard,  can  he  buy 
with  the  money  ? 

8.  Three  boys  have  some  marbles.     James  has   10, 
Henry  9,  and  John  4.     If  they  divide  them  equally,  how 
many  marbles  will  each  have  ? 

9.  How  many  days  work, at  4  dollars  a  day, will  pay  for 
3  tons  of  coal  worth  8  dollars  a  ton  ? 

EXEECISES   FOB  THE    SLATE   AND   BOARD. 

1.  Divide    32760  by  12  ;    by  13  ;    by  14  ;    by  15. 

2.  Divide  970640  by  23  ;    by  34  ;    by  25  ;    by  36. 
8.  Divide    40320  by  12  ;    by  24  ;    by  15  ;    by  16. 

4.  Divide  816480  by  24  ;    by  27  ;    by  35  ;    by  36. 

5.  Divide  445280  by  32  ;    by  41 ;    by  28  ;    by  33. 

6.  How  many  pounds  of  sugar, at  14  cents  a  pound,  will 
pay  for  13  pounds  of  butter, at  28  cents  a  pound  ? 

7.  How  many  pounds  of  coffee  worth  25  cents  a  pound, 
can  be  bought  for  15  bushels  of  oats  worth  65  cents  a 
bushel? 


124  FIRST     BOOK 

LESSON     CXIII. 

1.  A  boy  having  12  oranges  bought  C  more,  and  then 
sold  7  ;  how  many  had  he  left  ? 

2.  James  sold  his  sled  for  45  cents,  which  was  9  cents 
more  than  it  cost :  what  did  it  cost  ? 

3.  Belle  paid  8  cents  a  spool  for  7  spools  of  thread, 
and  9  cents  for  some  buttons  :  what  did  she  pay  for  both  ?- 

4-  Which  is  less,  7  times  8  or  6  times  9  ?  Which  is 
greater,  5  times  12  or  8  times  8  ? 

5.  What  will  be  the  cost  of  7  coats  at  12  dollars  each  ? 

6.  If  Jane  has  11  cents  and  Grace  has  G  times*  as  many, 
how  many  cents  has  Grace  ?     How  many  have  both  ? 

7.  If  John  has  40  marbles  and  Dick  has  1  fourth  as 
many,  how  many  marbles  has  Dick  ? 

8.  If  6  quarts  of  milk  cost  54  cents,  what  will  be  the 
cost  of  4  quarts  ?     7  quarts  ?     9  quarts  ?     8  quarts  ? 

9.  Willie  sold  his  knife  for  36  cents,  and  received  in 
payment  3  quarts  of  chestnuts  at  8  cents  a  quart,  and 
the  remainder  in  money ;  how  much  money  did  he  receive? 

10.  If  a  man  can  chop  16  cords  of  wood  in  8  days,  how 
much  can  he  chop  in  3  days  ?    In  5  days  ?     In  7  days  ? 
In  12  days  ? 

11.  How  many  barrels  of  flour  worth  8  dollars  a  barrel, 
will  pay  for  4  loads  of  hay  worth  12  dollars  a  load  ? 

12.  If  7  yards  of  cloth  cost  28  dollars,  what  will  5  yards 
cost? 

13.  If  1  yard  of  ribbon  cost  10  cents,  how  many  yards 
can  he  bought  for  60  cents?    For  70  cents?    For  90 
cents  ?    For  120  cents  ? 


IH     ARITHMETIC,  125 

LESSON     CXIV. 

EXERCISES  FOR  THE  SLATE  AND  BOARD. 

1.  The  greater  of  two  numbers  is  590,  and  the  less 
364  ;  what  is  their  difference  ? 

2.  The  less  of  two  numbers  is  128,  and  their  differ- 
ence is -75  ;  what  is  the  greater  ? 

3.  The  sum  of  two  numbers  is  405,  and  one  of  the 
numbers  is  214  ;  what  is  ike  other  ? 

4.  How  many  must  be  ;ui«led  to  24  to  make  56  ? 
5.*H6w  many  more  than    24  men  are  210  men  ? 

6.  How  many  less  than  i:2  sheep  are  27  sheep? 

7.  How  many  more  than  (::>  +  36  is  124  ? 

8.  How  many  less  than  i^- -1  +  153  is  246  ? 

9.  How  many  must  be  aaciea  to  74  +  127  to  make  304  ? 

10.  A  man  paid  3146  dollars  for  a  house,  which  was 
380  dollars  more  than  it  was  worth  ;   what  was  it  worth  ? 

11.  From  1705,  take  the  sum  of  540  and  603. 

12.  From  the  difference  of  3242  and  646  take  845. 

13.  Bought  a  house  for  5607  dollars,  which  was  825 
less  than  it  was  worth  ;  what  was  it  worth  ? 

H.  A  man  owed  756  dollars,  and  paid  at  one  time  206 
dollars,  and  at  another  time  324  dollars.  How  much  did 
he  still  owe  ? 

15.  Mr.  Smith  has  640  acres  of  land,  and  Mr.  Jones 
has  124  acres  less  ;  how  many  acres  has  Mr.  Jones  ? 

10.  From  a  bin  containing  394  bushels  of  oats,  248 
bushels  were  taken,  and  afterwards  86  bushels  returned  ; 
how  many  bushels  were  then  in  the  bin  ? 


126  FIRST     BOOK 

LESSON    CXV, 

EXERCISES  FO'R  THE  SLATE  A^D  BOARD. 

1.  If  a  steamer  sail  265  miles  a  day,  how  far  will  she 
sail  in  16  days  ?    In  18  days  ?    In  24  days  ? 

2.  A  man  bought  136  barrels  of  flour  at  8  dollars  a 
:  barrel,  and  sold  the  whole  for  1248  dollars.     What  was 

his  gain  ? 

-  3.  What  is  the  value  of  each  of  the  following  articles  : 
'  25  pounds  of  sugar  at  12  cents  a  pound ;  16  pounds  of 
tea  at  75  cents  a  pound ;  and  38  pounds  of  ham  at  14 
cents  a  pound  ? 

4»  What  is  the  value  of  the  whole  ?     How  much  more 
is  the  tea  worth  than  the  sugar  ? 

5.  How  many  tons  of  hay  worth  16  a  ton,  will  pay  for 
24:  cows  worth  32  dollars  each  ? 

6.  If  a  clerk  earn  a  salary  of  950  dollars  a  year,  and 
his  expenses  are  525  dollars  a  year,  how  much  can  he 
save  in  6  years  ? 

7.  A  farmer  sold  96  bushels  of  potatoes,  at  52  cents  a 
a  bushel.     How  many  pounds  of  coffee,  at  26  cents  a 
pound,  will  pay  for  the  potatoes  ? 

8.  If  24  yards  of  cloth  cost  144  dollars,  what  will  56 
yards  cost  at  the  same  rate  ? 

9.  A  farmer  sold  15  tons  of  hay,at  18  dollars  a  ton 
and  36  cords  of  wood,  at  4  dollars  a  cord  :  what  was  the 
value  of  both  ? 

10.  He  divided  the  whole  amount  of  money  equally 
among  6  creditors  :  how  much  did  each  receive  ? 


AEITHMETIC. 


LESSON    CXVI. 


L  Multiply      3417  by    9; 

2.  Multiply   10782  by  21; 

8.  Multiply   56043  by  32; 

4.  Multiply   28340  by  41 ; 

5.  Multiply  730081  by  44  ; 

6.  Multiply  186304  by  65  ; 

7.  Multiply  304071  by  46  ; 

8.  Multiply  415036  by  75  ; 

9.  Multiply  630400  by  46  ; 

10.  Multiply  297182  by  77  ; 

11.  Multiply  710345  by  68  ; 


by  12; 

by  14; 

by  16. 

by  18; 

by  26; 

by  19. 

by  25; 

by  36; 

by  27. 

by  29; 

by  46; 

by  37. 

by  53; 

by  38  ; 

by  54. 

by  67  ; 

by  55; 

by  49. 

by  72; 

by  84; 

by  66. 

by  63; 

by  54; 

by  82. 

by  57; 

by  68; 

by  74. 

by  94; 

by  95; 

by  89. 

by  77; 

by  81; 

by  93. 

LESSON    CXVI  I. 
Find  the  value  of 


1.  598467- 
2.  541604- 
S.  639514- 
4.  954632- 

-6. 
-8. 
-4. 

-7. 

5.  985478- 
6.  517401- 
7.^378487- 
£."371561- 

-7. 
-8. 
-9. 
-8. 

9.  6897583- 
10.  4996504- 
11.  1918575- 
12.  5982039- 

-5. 
-8. 
-6. 
-9. 

How  many  times 

18.  Is  13  contained  in  273  ?    In  4550  ?    In  36721  ? 

14.  Is  17  contained  in  £465?    In  50571  ?    In  12991 23? 

15.  Is  18  contained  in  10404  ?     In  7831  ?    In  11052  ? 
•«.  Divide  35280  by  25  ;  by  32  ;  by  27  ;  by  24. 

•17.  Divide  122764  by  36  ;  by  24;  by  28  ;  by  26. 

18.  Divide  7462450  by  42 ;  by  36  ;  by  52  ;  by  48. 


123 


FIEST     BOOK 


LESSON    CXV.III. 

1.  If  a  peach  is  divided  into  tivo  equal  parts,  one  of 
these  parts  is  called   one-half  of  a 

peach. 

2.  How  many  halves  make  one,  or  a 
whole  thing  ? 

3.  If  a  pear  is  divided  into  three  equal  parts,  one  of  these 
parts  is  called  one-third  of  a  pear. 

4.  How  many  thirds  make  one,  or  a 
whole  thing  ? 

5.  How  many  thirds  in  one  pear  ? 

6.  If  an  apple  is  divided  into  four  equal  parts,  one  of 
these  parts  is  called  one-fourth  of  an 

apple. 

7.  How  many  fourths  make  one,  or  a 
whole  thing  ? 

8.  If  an  orange  is  divided  into  five  equal  parts,  one  of 
these  parts  is  called  one-fifth  of  an  orange. 

9.  How  many  fifths  make  one,  or  a  whole 
thing? 

10.  One-half  is  written  £. 

11.  One-third  is  written  £  ;  two-thirds,  f .     One-fourth 
is  written  £ ;  two-fourths,  f ;  three-fourths,  |. 

12.  One-fifth  is  written  | ;  two-fifths,  f ;  three-fifths, 
f  ;  four-fifths,  | ;  five-fifths,  |. 


IN     ARITHMETIC.  129 

LESSON    CXIX. 

1.  One  whole  thing  is  equal  to  how  many  "halves  ? 
Thirds  f    Fourths  ?    Fifths  f    Sixths  t    Sevenths  ?  etc. 


unit. 
Two-halves. 


Five-fifths. 

Six-sixths. 

Seven-sevenths. 

Eight-eighths. 

.Nine-ninths. 

2.  When  anything  is  divided  into  six  equal  parts,  what 
is  one  part  called?     Two  parts?     Three  parts?    Four 
parts  ?    Five  parts  ? 

3.  What  is  one  of  the  seven  equal  parts  of  anything 
called  ?     Three  of  seven  equal  parts  ?    Five  of   seven 
equal  parts  ?     Six  of  seven  equal  parts  ? 

4.  What  is  meant  by  one-eighth  of  a  number  or  whole 
thing?  Ans.  One  of  the  eight  equal  parts  of  it. 

5.  What  is  meant  by  one-ninth  of  a  number  or  whole 
thing  ?     Two-ninths  ?    Five-ninths  9 

6.  What  is  meant  by  one-tenth  of  anything  ?   Six-tenths  9 

7.  How  many  sixths  make  a  whole  thing  ?     How  many 
sevenths?    Eighths?    Ninths?     Tenths? 


13C  FIRST     BOOK 

LESSON    CXX. 

1.  A  Unit  is  one,  or  a  single  thing. 

2.  Numbers  that  express  or  represent  equal  parts  of  a 
unit  are  called  Fractions;  as,  one-half  (£)  ;    two- 
thirds  (|),  etc. 

3.  A  fraction  is  expressed  by  two  terms  or  numbers, 
and  when  written,  one  is  placed  below  and  the  other  above 
a  short  line ;  as,  £,  -f,  -f,  etc. 

4-  The  number  below  the  line  is  the  Denominator. 

Thus,  in  the  fraction  f ,  4  is  the  denominator,  and  shows  that  the 
unit  is  divided  iufour  equal  parts,  named  fourths. 

5.  The  number  above  the  line  is  the  Numerator, 

Thus,  in  f ,  3  is  the  numerator,  and  shows  that  3  of-  the  4  equal 
parts  are  taken,  or  expressed,  by  the  fraction. 

6.  The  numerator  and  denominator  of  a  fraction  are 
called  the  Terms. 

Thus,  3  and  4  are  the  terms  of  the  fraction  f . 

7.  Eead  the  following  fractions,  and  name  the  denom- 
inator and  the  numerator  in  each : 

i    i    i    4>   i    t,    t,    i,    f,   A,    1- 

£.  Write  the  following  in  figures : 

Five-ninths.  Four-ninths.  One-twelfth. 

Three-sevenths.  Seven-ninths.  Five-elevenths. 

Two-fifths.  Seven-tenths.  Nine-fourteenths. 

Four-sevenths.  Five-sevenths.  Eleven -twelfths. 

Five-sixths.  Eight-ninths.  Eight-fifteenths. 

Three-eighths.  Nine-tenths.  Seven-twentieths. 


IK     ARITHMETIC.  Ul 

LESSON    CXXI. 

1.  How  do  you  find  one-half  of  any  number? 

Am.  Divide  the  number  by  2. 

2..  How  do  you  find  1  third  of  any  number  ?    £  ?    |  ? 
i?    I?    i?     i.?    j_?  etc. 

5.  What  is  I- of  6?     Of  8?     Of  12?     Of  18?     Of  20? 

4.  What  is  |  of  9?    Of  15  ?    Of  21  ?    Of  24?    Of  27  ? 

5.  What  is  i  of  12  ?    Of  16  ?    Of  28?    Of  32?    Of  40? 

6.  What  is  ^  of  20  ?    Of  35  ?    Of  45  ?    Of  50  ?    Of  60  ? 

7.  What  is  |  of  18?    \  of  21  ?  -|of30?    £  of  36  ? 

8.  What  is  |  of  28  ?    £  of  54  ?    £  of  48  ?    }  of  63  ? 
0.  What  is  £  of  40  ?    ^  of  45  ?    \  of  49  ?    £  of  72  ? 

i  of  56  ? 

4 

7(9.  What  do  you  understand  by  f  of  any  number  or 
tiling  ?  Ans.  Two  of  the  five  equal  parts  into  which  the 
number  or  thing  is  divided. 

11.  What  do  you  understand  by  f  of  any  number  or 
thing?    By  |?     By  i?    f?     By*?    f?    f?     By  £? 

I?    I?    1? 

12.  What  is  meant  by  %  of  any  number  or  thing  ?     By 

I?    t?    I?    1?     By^?    A?    A?    A? 

^.  What  is  |  of  12? 

SOLUTION.— Ofte-third  of  12  is  4  ;  2  thirds  of  12  are  2  times  4,  or  8. 
Hence  f  of  12  are  8. 

^.  What  is  f  of  16  ?    f  of  15  ?    f  of  20  ?    f  of  25  ? 

15.  What  is  f  of  18?    |  of  30?    f  of  21  ?    f  of  28  ? 
|  of  32  ?    f  of  36  ? 

16.  What  is  f  of  27  ?    f  of  18  ?    f  of  36  ?    ^  °f  4<>  ? 
ft-  of  30  ?    T\  of  44  ? 


132  FIRST     BOOK 

LESSON    CXXII. 

1.  How  do  you  find  how  many  halves  there  are  in  any 
whole  number?    Am.  Multiply  the  whole  number  by  2. 

2.  How  do  you  find  how  many  thirds  there  are  in  any 
number?       How    many  fourths?      Fifths?      Sixths? 
Sevenths?    Eighths?    Ninths?     Tenths?  etc. 

3.  How  many  halves  are  there  in  3  peaches  ? 

SOLUTION. — Since  in  1  peach  there  are  2  halves,  in  3  peache* 
there  are  3  times  2  halves,  or  6  halves.  Hence,  in  3  peaches  are 
6  halves.  * 

4.  How  many  halves  are  there  in  4  ?     In  8  ?    In  9  ? 

5.  How  many  thirds  are  there  in  5  ?     In  7  ?     In  8  ? 

6.  How  many  fourths  are  there  in  7?  fifths  in  8  ? 
sixths  in  6  ?    sevenths  in  9  ?    eighths  in  7  ?    ninths  in  5  ? 
tenths  in  8  ? 

7.  How  many  halves  in  one  and  a  half  ? 

SOLUTION. — In  1  are  2  halves,  and  1  half  added  makes  3  halves. 
Hence,  in  1  and  1  half  there  are  3  halves. 

8.  How  many  halves  in  3  and  1  ffalf  ?     In  5  and  1  half  ? 

9.  How  many  thirds  in  2  and  2  thirds  ? 

SOLUTION. — Since  in  1  there  are  3  thirds,  in  2  there  are  2  times 

3  thirds,  or  6  thirds,  and  2  thirds  added  make  8  thirds.    Hence,  in 
2  and  2  thirds  there  are  8  thirds. 

10.  How  many  thirds  in  4  and  1  third  ?  fourths  in  3 
and  1  fourth  ? 

11.  How  m%nj  fift-hs  in  2  and  3  fifths?   sixths  in  5  and 

4  sixths  ?  sevenths  in  3  and  2  sevenths  ? 

J?#.  How  m&nj  fourths  in  6  and  3  fourths  ?  In  7  and 
1  fourth  ?  In  8  and  3  fourths  ? 


IK     ARITHMETIC.  133 

LESSON    CXXIII. 

1.  When  the  numerator  and  denominator  of  a  frac- 
tion are  equal,  the  value  of  the  fraction  is  equal  to  1  ;  as 
J=l;  t=l;  f=l,  etc. 

2.  When  the  numerator  is  greater  than  the  denomina- 
tor, the  value  is  greater  than  1;  as  -£:=1-J;  f—  2,  etc. 

S.  A  whole  number  and  a  fraction  written  together  are 
called  a  Mixed  Number  ;  as  of,  read  5  and  3  fourths*. 

4*  Read  the  following  mixed  members  : 


5.  How  m&aj  fifths  are  4f  ? 

SOLUTION,  —  Since  in  1  there  are  5  fifths,  in  4  there  are  4  times 
5  fifths,  or  20  fifths,  and  3  fifths  added  make  23  fifths.  Hence 
4|  are  ^. 


6?.  How  many  fourths  are  9£  ?    Are  7|  ?    Are  8J  ? 

7.  How  many  £Mr^s  are  12f  ?  .M/Ms  are  6-J-  ?  Sixths 
are  7|  ?  Fourths  are  lOf  ? 

&  Change  4f  to  eighths;  9-f  to  sevenths;  8TV  to 
tewMs  ;  5|  to  ninths  ;  4^-  to  tivelfths. 

9.  How  many  owes  are  ^  ? 

SOLUTION.  —  Since  4  fourths  equal  1,  12  fourths  are  as  many  Ts 
as  4  fourths  are  contained  times  in  12  fourths,  or  3  times.  Hence 
if  are  3  ones  or  3.  Or  \2-=12-i-4=3. 

10.  Find  the  value  of  *£  ;  of  -1/  ;  of  ^  5  of  ¥  5  of  ^. 
^^.  Change  to  a  whole  or  a  mixed  number  -?/-  ;  -2/  ;  y  • 

V;  «;  -¥-; 


^.  What  is  the  value  of  ^  ?   4^?   ff?  -%°-?   f  o  ? 
^.  Find  the  value  of  ^  ;  ff  ;  ^  ;  -ff 


134  FIEST     BOOK 

LESSON    CXXIV. 

1.  How  many  are  %  fifths  and  3  fifths  9 

Ans.  5  fifths,  or  f—1. 

2.  Can  you  add  3  apples  and  5  figs 9     Why  not  ? 

3.  Can  you  add  3  fourths  and  5  sixths  9     Why  not  ? 
^.  Only  fractions  having  the  same  denominator  can 

be  added. 

5.  How  many  are  -J  +  f  ?  -4/w.  -^=11. 

0.  What  is  the  sum  of  f  and  £  ?     of  TV  and  -&  ?     Of 
|  and*?     Of^and^? 

7.  Add  -^  and  ^.     T7T  and  T8T.     f  and  -J.     f  and  £. 

8.  How  many  are  7  ninths  less  2  ninths  9 

Ans.  6  ninths,  or  f. 

9.  Can  you  take  6  books  from  9  s?#to  ?    Why  not  ? 
10.  Can  you   subtract   6   sevenths  from   9    twelfths  9 

Why  not  ? 

71.  Only  fractions  having  the  same  denominator  can  be 
subtracted. 

12.  How  many  are  f-f  ?  ^-yV  ?  TV~TV  ?  «- A  ? 

1&  Subtract  f  from  |.     TST  from  •&.     T4T  from  |f . 

1^.  How  many  are 

U.  Howmany  1's  are 

10.  From  | +  |  +  1  take  |. 

17.  From  1V  +  tV  +  ii  subtract  ^. 

18.  John  spent  f  of  his  money  and  lost  f  of  it.     What 
part  of  his  money  had  he  left  ? 

19.  James  paid  f  of  a  dollar  for  a  book,  and  f  of  a  dol- 
lar for  a  slate.     How  much  did  he  pay  for  both  ?     How 
much  more  for  the  book  than  for  the  slate  ? 


IX     ARITHMETIC.  135 

LESSON    CXXV. 

1.  If  a  cake  is  cut  into  12  equal  pieces,  what  part  of 
the  whole  cake  is  each  piece  ?  Ans.   One-twelfth. 

2.  How  many  twelfths  make  a  whole 
thing  ? 

3.  How  do  we  find  1  twelfth  of  any 
number  ? 

4.  If  a  cake  is  divided  into  3  equal  parts,  each  part  is 
called  1  third. 

5.  If  each  third  of  the  cake  is  di- 
vided into  4  equal  parts,    into   how 
many  parts  is  the  whole  cake  divided  ? 

6.  How  many  twelfths  in  1  third?  In  2  thirds?  3  thirds  ? 

7.  If  a  cake  is  cut  into  4  equal  parts,  each  part  is  called 
1  fourth. 

8.  If  each  fourth  of  the  cake  is  di- 
vided into  3   equal  parts,   into  how 
many  parts  is  the  whole  cake  divided  ? 

9.  How  many  tivelfths  in  1  fourth  ?    In  2  fourths  ?    In 
3  fourths  ?     In  4  fourths  ? 

10.  If  Edie  has  £  of  a  cake  and  Asa  J  of  it,  what  part 
have  both? 


SOLUTION.—  Since  \  is  equal  to  ^,  and  J  is  equal  to  T\,  they  have 
the  sum  of  T\  and  -f£,  or  T7¥. 

.7^.  How  much  more  has  Edie  than  Asa?    -J-—  J=  ? 

12.  How  many  twelfths  in  $  ?  In£?  Inf?  InJ?  Inf? 

13.  Which  is  greater  -J-  or  £  ?    £  or  |  ?    f  or  }  ? 

^.  If  Mary  has  £,  and  Jennie  £  of  a  melon,  what  part 
of  the  whole  melon  have  both  ? 


136 


FIBST     BOOK 


LESSON    CXXVI. 

1,  Draw  lines  upon  the  slate  or  board  of  equal  length, 
and  divide  them  into  12  equal  parts. 


2.  By  a  heavier  mark  these  lines  may  be  divided  into 
halves,  thirds,  fourths,  and  sixths,  respectively. 


8.  Hence,  it  is  plain  that  halves,  thirds,  fourths,  sixths, 
and  twelfths,  may  be  added  or  subtracted  when  changed 
to  parts  of  equal  size  or  magnitude. 

What  is  the  sum  of 

4.  $  and  |  ? 
6.  i-  and  ±  ? 
6.  1  and  4-  ? 


7.  |  and  f  ? 

8.  £  and  -^  ? 

9.  f  and  f  ? 

What  is  the  value  of 


10. 
11. 

12. 


£  and  £  ? 
-&•  and  |  ? 
f  and£? 


^.     4  — 


./£.     4  — 


.76.     f  —  | 


—     ? 


A- 


When  fractions  have  different  denominators,  they  must  be 
changed  to  fractions  of  like  value,  having  the  same  denominators, 
before  they  can  be  added  or  subtracted. 


IN    ARITHMETIC.  13? 

LESSON     CXXVII. 

1.  4  is  £  of  what  number  ? 

SOLUTION. — Since  4  is  1  half  of  a  number,  2  halves  or  the  nun^ 
ber  are  2  times  4,  or  8.    Hence  4  is  J  of  2  times  4,  or  8. 

£  5  is  £  of  what  number  ?  £  of  what  number  ? 
&  7  is  £  of  what  number  ?  £  of  what  number  ? 
4-  6  is  £  of  what  number  ?  -^  of  what  number  ? 
5.  4  is  £  of  what  number  ?  £  of  what  number  ? 
#.  8  is  £  of  what  number  ?  £  of  what  number  ? 

7.  3  is  ^  of  what  number  ?     ^  of  what  number  ? 

8.  If  £  of  a  ton  of  coal  cost  2  dollars,  what  will  1  ton  cost  ? 

9.  George  gave  a  beggar  6  cents,  which  was  -£  of  all 
the  money  he  had ;  how  much  money  had  he  ? 

10.  If  £  of  a  pound  of  coffee  cost  8  cents,  what  will  £ 
of  a  pound  cost  ? 

SOLUTION.— Since  1  fourth  of  a  pound  costs  8  cents,  3  fourths  of 
a  pound  will  cost  3  times  8  cents,  or  24  cents. 

11.  If  -J-  of  a  bushel  of  pears  cost  9  cents,  what  will  f  of 
a  bushel  cost  ? 

12.  In  -3*5-  of  a  dollar  are  10  cents ;  how  many  cents  in 
TV  of  a  dollar  ? 

13.  If  a  man  walk  6  miles  in  £  of  a  day,  how  many 
miles  can  he  walk  in  1  day  ? 

14.  A  pencil  cost  8  cents,  which  was  %  the  cost  of  a 
book  ;  what  was  the  cost  of  the  book  ? 

15.  If  -J-  of  a  melon  cost  7  cents,  what  will  f  of  it  cost  ? 
./#.  If  -J-  of  a  barrel  of  flour  is  worth  2  dollars,  what  is 

|  of  a  barrel  worth  ?    What  is  a  whole  barrel  worth  ? 


138  FIRST     BOOK 

LESSON     CXXVIII. 

1.  If  a  barrel  of  sugar  is  worth  24  dollars,  what  is  \  of 
it  worth  ?  2  thirds  ?  1  fourth  ?  3  fourths  ? 

£.  If  a  hoy  earns  10  dollars  in  a  week,  and  spends  2 
fifths  of  it,  what  part  is  left  ?  How  many  dollars  ? 

3.  When  coal  is  7  dollars  a  ton,  what  part  of  a  ton  will 
1  dollar  buy  ?     2  dollars  ?     3  dollars  ?     5  dollars  ? 

4.  At  |  of  a  dollar  a  yard,  what  will  4  yards  of  cloth  cost  ? 

SOLUTION.— Since  1  yard  costs  f  of  a  dollar,  4  yards  will  cost 
4  times  |  or  f  of  a  dollar,  equal  to  2|  dollars. 

5.  At  f  of  a  dollar  a  pound,  what  will  6  pounds  of 
butter  cost  ?    8  pounds  ?     9  pounds  ? 

6.  How  many  are  3  times  f  ?    2  times  $  ?    4  times  -J-  ? 

7.  How  many  are  5  times  f  ?    6  times  f  ?    7  times  -J-  ? 
£.  "What  is  the  difference  between  3  fourths  of  24  and 

4  fifths  of  30  ?     2  thirds  of  27  and  1  sixth  of  60  ? 

9.  If  a  ton  of  hay  cost  21  dollars,  what  will  3  sevenths 
of  a  ton  cost  ?  2  thirds  of  a  ton  ? 

10.  A  boy  having  20  marbles,  gave  }  of  them  to  one 
companion,  and  \  to  another  ;  how  many  had  he  left  ? 

11.  Jane  paid  25  cents  for  a  book,  and  f  as  much  for  a 
slate ;  what  did  she  pay  for  the  slate  ? 

12.  Fanny  is  14  years  old,  and  her  sister  is  f  as  old  : 
how  old  is  her  sister  ? 

13.  What  will  be  the  cost  of  6  boxes  of  figs,  at  |  of  a 
dollar  a  box  ? 

14.  If  1  pineapple  cost  f  of  a  dollar,  what  will  4  pine- 
apples cost?    What  will  G  cost  ?     8?     9?    10? 


IK     ARITHMETIC.  139 

LESSON    CXXIX. 

1.  How  many  oranges  in  6  thirds  of  an  orange  ?    In  7 
thirds  ?     In  9  thirds  ?     In  10  thirds  ? 

2.  How  many  yards  in  -J  of  a  yard  ?    In  $  of  a  yard  ? 
In -LA?     In-^?     In-^? 

3.  If  3  books  cost  12  fif  fchs  of  a  dollar,  what  will  1  book 
cost? 

SOLUTION. — Since  3  books  cost  12  fifths  of  a  dollar,  1  book  will 
cost  1  third  of  12  fifths,  or  4  fifths  of  a  dollar. 

4.  If  3  pounds  of  coffee  cost  -f$  of  a  dollar,  what  will 
1  pound  cost  ?     What  will  5  pounds  cost  ? 

6.  If  4  yards  of  ribbon  cost  f  of  a  dollar,  what  will  3 
yards  cost  ?  5  yards  ?  7  yards  ?  10  yards  ? 

6.  If  a  man  walks  f  of  6  miles  in  1  hour,  how  far  can 
he  walk  in  3  hours  ?     How  far  in  -J  of  an  hour  ? 

7.  If  5  bushels  of  oats  are  worth  -^  of  a  dollar,  what  is 
1  bushel  worth  ?     3  bushels  ?     G  bushels  ?     10  bushels  ? 

8.  If  3  fourths  of  a  bushel  of  cranberries  are  worth 
3  dollars,  what  is  -J-  of  6  bushels  worth  ? 

9.  At  4  dollars  a  yard,  what  will  2%  yards  of  cloth  cost  ? 

SOLUTION.— Since  1  yard  costs  4  dollars,  2 J  yards  will  cost  2| 
times  4  dollars  ;  2  times  4  dollars  are  8  dollars,  and  |  of  4  dollars 
is  2  dollars,  which  added  to  8  dollars  make  10  dollars.  Hence  2J- 
yards  will  cost  10  dollars. 

10.  At  10  dollars  a  barrel,  what  will  £  barrel  of  flour 
cost  ?     What  will  $  of  a  barrel  cost  ?     2|  barrels  ? 

11.  At  f-  of  16  cents  a  pound,  what  will  \  of  a  pound 
of  sugar  cost  ?    |  of  a  pound  ?    1  £  pounds  ?    2±  pounds  ? 


140 


J?iKST     BOOK 


LESSON    CXXX. 

1.  In  measuring  a  quantity,  some  definite  part  of  it  is 
taken  as  a  Unit  of  Measure  ;  as,  a  yard,  a  gallon,  etc., 
by  which  all  quantities  of  that  kind  are  measured. 

Hence,  the  length  of  a  piece  of  cloth  is  ascertained  by  applying 
a  yard  measure ;  the  capacity  of  a  cask  by  the  use  of  a  gallon 
measure ;  the  weight  of  a  body  by  the  pound  weight,  etc. 

2.  Measures  may  be  classified  into  six  kinds  :  Money  or 
Value,  Extension,  Capacity,  Weight,  Time,  Angles  or  Arcs. 


MONEY. 

3.  Money  is  the  measure  of  the  value  of  things. 

4.  The  legal  money  of  this  country  is  called  United 
States  Money. 

5.  The  Gold  Dollar  is 

the   unit   of    United    States 
Money. 


10  Mills  (m.)    = 
10  Cents 
10  Dimes 

100  cents  =  1  dollar  ; 
25  cents  =  J  dollar ; 


TABLE. 

1  Cent    .     .  ct. 
1  Dime   .    .  d. 
1  Dollar      .  $. 
75  cents  =  f  dollar ; 
20  cents  =  J-  dollar  ; 


/ 1000  m. 
;1  =  •]    100  ct. 

(     10  d. 

50  cents  =  |  dollar ; 
12|  cents  =  J  dollar. 


The  money  of  the  Dominion  of  Canada  is  the  same  as  that  of  the 
United  States. 


IK     ARITHMETIC.  141 

LESSON    CXXXI. 

1.  How  many  milffe  in  1  cent  ?    3  cents  ?    5  cents  ? 

2.  How  many  cents  are  30  mills  ?  50  mills  ?  60  mills  ? 

3.  How  many  dimes  are  20  cents  ?    40  cents  ? 

4.  How  many  cents  are  3  dimes  ?  4  dimes  ?   6  dimes  ? 

5.  How  many  dimes  in  1  dollar  ?     How  many  cents  ? 
&  In  half  a  dollar,  how  many  dimes  ?     Cents  ? 

7.  How  many  cents  are  1  dollar  ?     2  dollars  ? 
6*.  How  many  cents  in  1£  dollars?     2 £  dollars? 
P.  How  many  dollars  in  200  cents  ?   In  150?    In  450? 
10.  The  sign  $  signifies  dollar  or  dollars,  and  is 
placed  before  the  number.    Thus  $3  means  three  dollars  ; 
$14  means  14  dollars,  etc. 

17.  When  dollars  and  £0%<te  are  written  together,  they 
are  separated  by  a  dot  ( , ) ;  thus,  $3.75  means  3  dollars 
and  75  cents. 

12.  When  cents  alone  are  expressed,  the  dot  is  placed 
after  the  sign  $  and  before  the  number;  thus,  $.50  is 
50  cents ;  $.18  is  18  cents,  etc.     Or  we  may  write  the 
word  cents  or  cts.  after  the  number ;  thus,  50  cents. 

13.  Mills  are  written  after  cents  ;  as,  $4.375  is  4  dol- 
lars 37  cents  5  mills.  5  mills  are  £  cent ;  $4. 3 75  =  $4. 3 7$. 

H.  Eead  the  following  : 

$3.46  $.375  $15.03  $1.12$ 

$4.50  $6.08  $10.10  $.796 

$7.62  $.427  $25.625          $.075 

15.  When  the  cents  are  less  than  10,  a  cipher  must  be 
placed  before  them  and  after  the  dot;  thus,  eight  cents 
is  written  8  cents,  or  $.08  ;  six-  cents,  6  cents,  or  $.06,  etc. 


142  FIBSTBOOK 

LESSON    CXXXII, 
EXERCISES  FOK  THE  SLAT^  AND  BOAKD. 
Write  in  figures 

1.  Forty-four  dollars  and  twenty-six  cents. 

2.  Eighteen  dollars  and  seventy-five  cents. 

8.  Thirty-five  cents.  6.  Fifteen  cents. 

4.  Eighty-seven  cents.  7.  Nine  cents. 

5.  Sixty  cents.  8.  Twenty  cents. 

9.  Seventy-eight  dollars  sixty-two  cents  and  five  mills, 

10.  One  hundred  fourteen  dollars  and  ninety  cents. 

11.  In  adding  and  subtracting,  dollars  should  be  placed 
under  dollars,  and  cents  under  cents,  so  that  the  dots 
may  be  in  the  same  column. 

Add  the  following  : 

W             (IS.)  (14.)            (15.) 

$3.50            $19.37  $6.29            $.875       . 

12.48                  .84  23.82  1.065 

_._75                5.09  1.10  12.63 

Arrange  in  columns  and  add  : 

16.  $11.36,  $26.07,  $9.16,  $32.76,  and  $2,34. 

17.  $42,06,  $10.30,  $4.82,  $.77,  and  $.93. 
Subtract  the  following : 

(18.)  (19.)  (20.)  (21.) 

From          $17.48  $73.26  $50.67  $120.80 

Take  6.27  25.18  10.08  35.26 


Find  the  value  of 
22.  $57.10  —  $12.40. 
28.  $104.47  -  $73.92. 


24.  $100.375  —  $40.095. 
26.  $416.08  -  $208.67. 


I  tf     ARITHMETIC.  143 

Find  the  sum 

26.  Of  $32.50,  $126.085,  $9.408,  $15.74,  and  $140. 

27.  Of  $307.09,  $50,  $6.848,  $100.10,  and  $450. 

28.  Of  $76,  $400,  $5.125,  $17.04,  $.975,  and  $1.625. 

29.  A  lady  paid  $45.40  for  a  dress,  $15.37fc  for  a  bon- 
net, $6  for  a  pair  of  gaiters,  and  $1.625  for  a  pair  of 
gloves.     What  did  she  pay  for  all  ? 

50.  A  farmer  sold  a  cow  for  $36.50,  a  ton  of  hay  for 
$14.25,   and  a  tub  of  butter  for  $20.80.     What  did  he 
receive  for  all  ? 

51.  Bought  aliat  for  $4.75,  a  pair  of  shoes  for  |5.125, 
a  paijrof  gloves  for  $.87J,  and  an  umbrella  for  $2.75. 
Wmre  ^jfts  the  cost  of  the  whole  ? 

Find  the  difference  between 


52.  $46.75  and  $14.45. 

53.  $142.09  and  $68.36. 


34.  $300.085  and  $104.50. 

35.  $87.875  and. $5.10. 


36.  $250 +  $2.75  and  $124.50. 

37.  $617.10 +  $50.125  and  $10.37^. 
S8.  $908.46  and  $325 +  $5.25. 

39.  $1263.18  and  $27.625 +  $114.37J. 

40.  A  man  bought  a  horse  for  $150,  and  sold  him  for 
$137.50.    What  did  he  lose  ? 

41.  A  grocer  paid  $28.75  for  a  barrel  of  sugar  and  sold 
it  for  $34.    What  did  he  gain  ? 

42.  Bought  a  sack  of  flour  for  $1.75,  a  pound  of  tea 
for  $.90,  and  some  sugar  for  $2.25.     How  much  must  I 
receive  in  change  for  a  5-dollar  bill  ? 

43.  Paid  $450  for  a  pair  of  horses,  and  sold  one  of  them 
for  $275.50.     What  did  the  other  cost  me  ? 


144  FIRST     BOOK 


Find  the  value 

44-  Of  $93.67—112.80. 

45.  Of  $118.19— $9.87f 

46.  Of  1500  — $300.277. 

47.  Of  $76.84£— $40.12-i-. 


48.  Of  $125 -$75 +  $14.50. 

49.  Of  $9.10  +  $46.08— $25. 

50.  Of  $48— $12.50— $13.92. 

51.  Of  $310 -$7.10 -$200. 


52.  A  farmer  sold  a  ton  of  hay  for  $12.50,  and  a  cord 
of  wood  for  $3.25.     He  received  in  payment  a  barrel  of 
flour  worth  $7.60,  and  the  remainder  in  money.    How 
much  money  did  he  receive  ? 

53.  A  grocer  sold  some  tea  for  80  cents,  some  butter 
for  2  dollars  30  cents,  some  eggs  for  53  '^cents,  and  some 
sugar  for  one  dollar  and  ten  cents.     How  much  change 
should  he  return  for  a  five-  dollar,  bill  ? 

54.  Mary  went  shopping  and  had  2  five-dollar  bills ;  she 
bought  a  dress  for  7  dollars  25  cents,  trimmings  for  2 
dollars  37£  cents,  some  thread  for  12|  cents,  and  some 
tape  and  needles  for  twenty  cents.     How  much  money 
had  she  left  ? 

55.  Henry  gave  one  dollar  and  a  half  for  a  pair  of 
skates,  seventy-five  cents   for  a  cap,  thirty-seven  cents 
for  a  ball,  half  a  dollar  for  a  knife,  two  dollars  and  a 
quarter  for  a  sled,  and  had  one  dollar  left.     How  much 
money  had  he  at  first  ? 

56.  A  man  owed  $427.50.    He  paid  at  one  time  $125.75, 
at  another  $100,  and  at  another  $50.25.     What  remained 
unpaid  ? 

57.  James  had   $5.48,    Henry  had  $1.17   more   than 
James,  and  George  had  $.75  less  than  James  and  Henry 
together.    How  much  money  had  George  ;  and  how  much 
had  they  all  ? 


IN     ARITHMETIC.  145 

58.  At  $5.75  a  ton,  what  will  5  tons  of  coal  cost  ? 

$5.75  ANALYSIS.  —  Since  1  ton  costs  $5.75,  5  tons  will 

5          cost  5  times  $3.75,  or  $28.  75. 

When  the   multiplicand   contains  cents,   put  the 


, 

$28.75          p0int  (,)in  the  product  two  places  from  the  right, 
and  prefix  the  sign  (  $  )  to  the  whole. 


(59.) 

(60.) 

(61) 

(6?.) 

Multiply    $24.32 

$42.09 

76  cents. 

$1.87 

By                        4 

5 

8       . 

6 

Product      $97.28 

$210.45 

$6.08 

$11.22 

In  like  manner, 

63.  Multiply  $326^by  5  ;  by  7  ;  by  8  ;  by  9  ;  by  12. 

64.  Multiply  $64.25  by  6  ;  by  8  ;  by  7  ;  by  9. 

65.  Multiply  $85.36  by  12  ;  by  14  ;  by  16  ;  by  24. 

66.  Multiply  $248.08  by  25  ;  by  26  ;  by  34  ;  by  42. 
Find  the  cost 

67.  Of  7  barrels  of  flour,  at  $8.60  a  barrel. 

68.  Of  22  yards  of  cloth,  at  $4.35  a  yard. 

69.  Of  40  bushels  of  wheat,  at  $1.75  a  bushel. 

70.  Of  13  pounds  of  tea,  at  $1.10  a  pound. 

71.  Of  27  pounds  of  butter,  at  33  cents  a  pound. 

72.  Of  34  barrels  of  potatoes,  at  $3.75  a  barrel. 

78.  At  $4.15  a  box,  what  are  18  boxes  of  oranges  worth  ? 

74.  At  $.875  a  pound,  what  are  16  pounds  of  tea  worth  ? 

75.  A  farmer  sold  6  cords  of  wood  at  $4.25  a  cord,  and 
18  barrels  of  apples  at  $3.15  a  barrel.     What  did  he  re- 
ceive for  both  ? 

76.  A  merchant  bought  25  yards  of  cloth  at  $3.50  a 
a  yard,  and  sold  it  for  $4.15  a  yard.     What  was  his  gain  ? 


146 


FIRST     BOOK 


77.  If  G  pounds  of  tea  cost  $7.50,  what  costs  1  pound  ? 

Divisor.  Dividend.  ANALYSIS. — Since  6  pounds  cost  $7.50 

6  )  $  7 .  5  0  1  pound  costs  1  sixth  of  $7.50,  or  $1.25. 

T"~    ~  When  the  dividend  contains  c^nts,  put 

Quotient  tlie  point  ^  iu  thc  quotient  two  piaces 

from  the  right,  and  prefix  the  sign  ($;  to  the  whole. 


In  like  manner  divide  the  following 
(78.)  (79.)  (80.) 

8)  $124.96        7)  $6.58        5)  $19.70 

$3.94 


$15.62 


$.94 


(81.) 

9)  $376.02 
$41.78 


82.  Divide  $705.60  by  4  ;  by  5  ;  by  6  ;  by  7. 


What  is 

87.  \  of  67344  inches  ? 

88.  |  of  437868  feet? 
99.  |  of  134860  pounds? 
90.  i  of  $1046.85  ? 


Find 

83.  I  fifth  of  $461.50. 

84.  1  eighth  of  $17.36. 

85.  1  seventh  of  $243.04. 

86.  1  sixth  of  $500.10. 

91.  Paid  $57.75  for  8  sheep.     What  did  each  cost  ? 

92.  If  6  tons  of  coal  cost  $40.80,  what  costs  1  ton  ? 

98.  Paid  $9.88  for  13  pounds   of  tea.     What  did  1 
pound  cost  ? 

Find  the  value 

94.  Of  $35.50-^4x12.  97.  Of  $90x18-^12. 

95.  Of  $4.35-^3x30.  98.  Of  $6.26x24^-8. 
96.. Of  $56.80^-8x19.  99.  Of  $12.75  x  14^-7. 

100.  If  5  boxes  of  lemons  are  worth  $23.25,  what  are 
14  boxes  worth  ? 

101.  If  6  books  cost  $1.90,  what  will  27  books  of  the 
same  kind  cost  ? 


IN     ARITHMETIC, 


147 


LESSON    CXXXIII. 

1.  English  or  Sterling  Money  is  the  money  of 
Great  Britain. 


2.  The  Sovereign, 
or  Pound  Sterility, 

is  the  unit  of  English 
Money. 

TABLE. 


4  Farthings  (far.)   =   1  Penny    .     .    .    .  d. 
12  Pence  =    1  Shilling      .    .    .  s. 
20  Shillings  =    1  Pound    ....£. 

The  value  of  a  Sovereign  in  United  States  Money  is  $4866^. 
2  Shillings  (s.)          =    1  Florin    .    .     .     .  fl. 

5  Shillings  =   1  Crown    .    .    .    .  cr. 


S.  French  Money  is  the  money  of  France. 


4.    The    Silver 
Franc  of  the  EE- 

PUBLIC  is  the  unit 
of  French  Money. 


The  value  of  a  Franc  in  United  States  Money  is  $.  193. 

TABLE. 

10  Millimes  (m.)  =  1  Centime  .  .  .  ct. 
10  Centimes  =  1  Decime  .  .  .  dc. 
10  Decimes  —  1  Franc  ....  fr. 


148  FIRST     BOOK 

LESSON    CXXXIV. 

1.  The  New  Empire  of  Germany  has  adopted 
a  new  and  uniform  system  of  coinage. 

2.    The    Reichs- 

marU  is  the  unit  of 
this  new  German  sys- 
tem of  Coinage. 

The  value  of  a  Keiclismark  ("  Mark")  in  U.  S.  Money  is  $.238. 

A  pound  of  gold  .900  fine  is  divided  into  139 J-  pieces,  and  the  ^ 
part  of  this  gold  coin  is  called  a  "Mark,"  and  this  is  subdivided 
into  100  pennies  (Pfennige). 

1.  How  many  farthings  in  2  pence?    In  4  pence? 
In  6  pence  ?     In  10  pence  ?    In  1  shilling  ? 

2.  How  many  pence  in  2  shillings  ?    In  3s.  ?    In  a 
florin  ?     In  a  crown  ? 

3.  How  many  shillings  in  3  florins  ?    In  4  crowns  ? 

4.  How  many  shillings  are  equal  to  half  a  sovereign  ? 
How  many  florins  ?    How  many  crowns  ? 

5.  What  is  the  value  of  a  sovereign  in  U.  S.  Money  ? 

6.  What  part  of  a  pound  is  half  a  sovereign  ?    Are  5 
florins  ?    Are  2  crowns  ? 

7.  How  many  centimes  in  1  franc  ?     In  5  francs  ? 

8.  What  part  of  a  franc  are  50  centimes  ?   25  centimes  ? 

9.  What  is  the  value  of  a  franc  in  U.  S.  Money  ? 

10.  Into  how  many  parts  is  a  mark  divided?    What 
are  they  called  ? 

11.  What  is  the  value  of  a  mark  in  U.  S.  Money  ? 


ARITHMETIC. 


149 


LESSON    CXXXV. 

1.  Extension  has  one  or  more  of  the  dimensions, 
length,  breadth,  and  thickness. 

2.  It  may  be  a  line,  a  surface,  or  a  solid. 

3.  A  Line  has  only  one  dimension — length. 

4-  Linear  Measure,  called  also  Long  Measure, 
is  used  in  measuring  lines,  or  distances. 


TABLE. 

12    Inches  (in.)  =  1  Foot   .  .  .  ft. 

3    Feet  =  1  Yard  .  .  .yd. 

5}  Yards,  or  16|  Ft.  =  1  Rod    .  .  .  rd. 

320    Rods  -  1  Mile    .  .  mi. 


1  Mi.  =  - 


63360  in. 

5280 /^. 

1760  yd. 

320  rd. 


5.  In  measuring  roads,  and  boundaries  of  land, 


7.92  Inches  =  1  Link    ....?. 

25  Links  =  1  Rod     .    .    .     .  rd. 

4  Rods  =  1  Chain  .     .     .     .  ch. 

80  Chains  =  1  Mile    ....  mi. 


63300  in. 
8000  I. 
320  rd. 
SOch. 


150  FIRST     BOOK 


LESSON    CXXXVI. 

1.  In  measuring  goods  sold  by  the  yard,  the  yard  is 
divided  into  halves,  fourths,  eighths,  and  sixteenths. 

2\  Inches  =  1  Sixteenth,  -fa  yd. 

2  Sixteenths   (44  in.)  =  1  Eighth,  J  yd. 

2  Eighths  (9  in.)  =  1  Quarter,  J  yd. 

4  Quarters  =  1  Yard,  1  yd. 

OTHER  DENOMINATIONS. 

4  Inches  =  1  Hand,       Used  to  measure  height  of  horses. 

6  Feet  =  1  Fathom,      "  depth      at  sea. 

I.lo2|  Statute  Miles  =  1  Geog.  Mi,    "  "          distances" 

3  Geographic  Miles  —  1  League. 

69. 16  Common  Miles  =  1  Degree. 

360  Degrees  =  The  Circumference  of  the  Earth. 


2.  The  units  of  linear  measure  are  lines. 

3.  This  line         1       I    i    I    i    I  is  one  inch  long. 

4.  The  inch  is  divided  into  halves,  fourths,  and  eighths. 

5.  Make  a  line  twice  as  long  ;  three  times  as  long. 

6.  How  many  inches  long  is  this  line  ? 


7.  How  many  inches  in  a  line  1  foot  long  ?    In  1  ft. 
6  in.  ?    In  2  ft.  ?     In  2  ft.  8  in.  ? 

8.  How  many  inches  in  one-half  ivoi  ?    In  one-third 9 

9.  How  many  feet  in  15  inches  ?  Ans.  1  ft.  and  3  in. 

10.  How  many  feet  in  18  inches?     In  36  inches? 

11.  How  many  inches  in  2  feet  ?     In  1  yard  ? 

12.  In  2  yards,  how  many  quarters  ?    Eighths  ? 


ARITHMETIC. 


151 


LESSON    CXXXVII. 

1.  Surface    or  Square    Measure   is   used  in 
measuring  surfaces  ;  as  of  land,  bfrards,  plastering,  etc. 


TABLE. 

144    Square  Inches  (sq.  in.)  —  1  Square  Foot 


9  Square  Feet 

30J  Square  Yards 

160  Square  Rods 

640  Acres 

36  Square  Miles 

sq.  mi.  A.          sq.  rd. 

-j    


.  sq.ft. 

=  1  Square  Yard    .     .  sq.  yd. 

=  1  Sq.  Rod  or  Perch,  sq.  rd.  ; 

=  1  Acre   .     ....  A. 

—  1  Square  Mile     .     .  sq.  mi. 

=  1  Township    .     .     .  Tp. 


sq.  yd. 


sq.ft. 


A.          sq.  ra.  sq.  ya.  sq.  jt. 

640   =   102400   =   3097600   =   27878400   = 

2.  In  computing  the  area  or  contents  of  land, 


sq.  in. 
4014489600 


625  Sq.  Links  (sq.  1.)  =  1  Pole     .     .  P. 
16  Poles  =  1  Sq.  Chain,  sq.  ch. 

10  Square  Chains    =  1  Acre    .     .A. 


1A 


100000  I. 
160  P. 
10  sq. 


152 


FIEST     BOOK 


SQUARE?  INCH 


1  Inch. 


1  yd.  or  3  ft. 


LESSON    CXXXVIII. 

1.  A  Surface  has  two  dimensions — length  and  Ireadth. 

2.  The  units  of  square  measure 
are  squares. 

3.  A  Square  is  bounded  by  four 
equal  sides. 

This  drawing  is  a  square  inch,  each  side 
of  which  is  1  inch  long. 

4.  How  many  square  inches  in  a 

strip  of  board  1  inch  wide  and  12  inches  long  ?     In  2  such 
strips?  In3?  In 4?  In5?  In 6?  7?  8?  9?  10?  11?  12? 

5.  A  square  yard  is  a  square,  each 
side  of  which  is  1  yd.,  or  3  ft.  long. 

This  drawing  represents  a  square  yard 
divided  into  square  feet. 

6.  In  1  row  there  are  3  sq.  ft.,  in 
3  rows  there  are  3  times  3  sq.  ft.,  or 
9  square  feet. 

7.  How  many  square  feet  in  the 
surface  of  a  table  3  feet  wide  and  6  feet  long? 

8.  How  many  square  feet  in  the  floor  of  a  room  8  ft 
wide  and  10  ft.  long  ? 

9.  How  many  square  feet  in  a  hall  6  ft.  wide,  1%  ft. 
long  ?     How  many  square  yards  ?     How  many  yards  of 
carpet  1  yd.  wide  will  cover  it  ? 

10.  How  do  we  find  the  surface  or  contents  of  a  square 
or  of  an  oblong  figure  ? 

Ans.  By  multiplying  together  the  two  dimensions,  or 
the  length  and  breadth. 


SQUAREWtARD 


3  eq.  ft.  x  3  =  9  sq.  ft. 


ABITHMETIC. 


153 


LESSON    CXXXIX. 

1.   Cubic  or  Solid  Measure  is  used  in  measuring 
solids  ;  as  timber,  wood,  stone,  boxes  of  goods,  etc. 

TABLE. 

1728  Cubic  In.  (cu.  in.)—l  Cubic  Ft,  cu.ft.  -j          ^  _  j  46656  cu.  in. 
27  Cubic  Feet  =1  Cubic  Yd.,  cu.  yd.  '  ~  (       27  cu.ft. 

%.  A  Solid  has  three  dimensions — length,  breadth,  and 
thickness. 

3.  The  units  of  cubic  measure  are  cubes. 

4.  A    Cube    is    a    body 
bounded  by  six  equal  squares 
called  faces. 

5.  The  sides  of  the  squares 
are  called  the  edges  of  the  cube. 

This  drawing  represents  a  cubic 
incli,  each  edge  of  which  is  1  inch 


154 


BOOK 


LESSON    CXL. 

1.   Wood  Measure  is  used  to  measure  wood  and 
rough  stone. 

TABLE. 


16     Cubic  Feet  =   1  Cord-Foot 

8     Cord-Feet,  or)     - 
128    Cubic  Feet     ) 


.  cd.ft. 


24f  Cubic  Feet          =  1  \  Perch  of  Stone-  '     Pch. 
(    or  of  Masonry  ) 

2.  A  pile  of  wood  8  feet  long,  4  feet  wide,  and  4  feet 
high  contains  1  cord. 

3.  One  foot  in  length  of  such  a  pile,  that  is,  1  foot  long, 
4  feet  wide,  and  4  feet  high,  is  called  1  cord-foot. 

4.  A  Perch  of  stone  or  of  masonry  is  16^  feet  long,  1-J- 
feet  wide,  and  1  foot  high,  and  contains  24J  cubic  feet. 


IN     ARITHMETIC.  155 

LESSON    CXLI. 

1.  How  many  cubic  feet  in  a  piece  of  timber  1  foot 
square  at  the  ends  and  3  feet  long  ?    In  2  such  pieces  ? 

2.  How  many  cubic  feet  in  4  such  pieces  ?     5  ?     G  ? 

3.  How  many  cubic  feet  in  1  cubic  yard  ?     In  2  cu.  yd.  ? 

4.  A  cubic  yard  is  a  cube  each  face  of  which  is  1  sq.  yd., 
and  each  edge  1  yd.,  or  3  ft.,  long.  g  feet 

This  drawing  represents  a 
cubic  yard,  each  face  being  a 
square  yard,  containing  9  sq.  ft. 

If  a  piece,  or  section,  1  foot 
thick  is  cut  from  one  side,  it  may 
be  divided  into  3  times  3  cu.  ft., 
or  9  cu.  ft.  And  since  a  cubic 
yard  contains  3  such  sections, 
there  are  3  times  9  cu.  ft.,  or  27  9  ca-  ft- x3  =  27  cu- 1U 

cu.  ft.,  in  a  cubic  yard. 

5.  How  many  cubic  feet  in  a  block  of  marble  1  ft. 
thick,  3  ft.  wide,  and  6  ft.  long?     2  ft.  wide,  2  ft.  thick, 
and  4  ft.  long  ? 

6.  How  many  inches  in  a  cubic  block  whose  edges  are 

3  inches  long?     Are  4  inches  long? 

7.  How  do  we  find  the  solidity,  or  contents,  of  a  cube 
or  of  an  oblong  body  ? 

Ans.  By  multiplying  together  the  three  dimensions,  or 
the  length,  breadth,  and  thickness. 

8.  How  many  cubic  feet  in  a  pile  of  wood  8  ft.  long, 

4  ft.  wide,  and  4  ft.  high?     In  a  pile  6  ft.  long,  5  ft. 
wide,  and  3  feet  high  ? 

9.  If  a  stove  bum  1  cord-foot  of  wood  in  a  week,  in 
what  time  will  it  burn  1  cord  ?    2  cords  ?    3  cords  ? 


156 


EIBST     BOOK 


LESSON    CXLII. 

L  Capacity  signifies  extent  of  room  or  space. 

2.  Measures  of  capacity  are  divided  into  two  classes  ; 
Measures  of  Liquids  and  Measures  of  Dry  Substances. 

3.  TAqiiid  Measure  is  used  in  measuring  liquids ; 
as  spirituous  liquors,  oil,  molasses,  milk,  water,  etc. 


TABLE. 

4    Gills  (gi.)  =  1  Pint  .    .    .  pt. 

2    Pints          =  1  Quart     .     .  qt. 

4  Quarts  =  1  Gallon  .  .  gal. 
31 1  Gallons  =  1  Earrel  .  .  Hbl. 
63  Gallons  —  1  Hogshead  .  hhd.  \ 


[  2016  gi. 
504.pt. 

1  Md.  =    1     252  qt. 
63  gal 
[       2  W. 


In  some  of  the  New  England  States  the  barrel  is  estimated  at 
32  gallons  ;  in  some  States  31  *  gallons,  and  in  others  from  28  to  32. 

4.  In  prescribing  and  compounding  liquid  medicines, 

61440. 
_  J  /3    1024. 


60  Minims  (til)    =  1  Fluidrachm  .  fi . 
8  Fluidrachms  =  1  Fluidounce   .  /J  . 


16  Fluidounces  =  1  Pint      ...  0. 
8  Pints  =  1  Gallon  .    .    .  Cong. 


Cong,  1  = 


fl 

0. 


128. 
8. 


ARITHMETIC. 


15? 


LESSON    CXLIII. 

1.  Dry  Measure  is  used  in  measuring  articles  not 
liquid  ;  as  grain,  fruit,  salt,  roots,  etc. 

TABLE. 


2  Pints  (pt.)  =  1  Quart  .  .  .  qt. 
8  Quarts  -  1  Peck  .  .  .  pk. 
4  Pecks  =  1  Busliel  .  lu. 


2.  The  weight  of  the  bushel  of  certain  grains,  seeds,  and 
vegetables  has  been  fixed  in  many  of  the  States  by  law, 
and  though  not  uniform  in  this  respect,  the  following  are 
the  prevailing  standards  : 


Wheat 

.   .  60  Ib. 

Beans  .... 

60  Ib. 

Wheat  Bran  . 

.  20  Ib. 

Rye    . 

.   .  56  " 

Buckwheat    . 

.  42  « 

Rye  Meal    .   . 

.  56  " 

Corn  . 

.   .  56  " 

Flax  Seed  .   . 

.  56  " 

Corn  Meal  .   . 

.  50  " 

Barley 

.   .  48  " 

Hemp  Seed   . 

.  44  " 

Corn  in  Ear    . 

.  68  " 

Oats    . 

.   .  32  " 

Potatoes     .   . 

.  60  " 

Clover  Seed    . 

.  60  " 

Peas  . 

.  .  60  " 

Onions    .  .  . 

.  5?  " 

Timothy  Seed 

.  45  " 

158  FIEST     BOOK 

LESSON    CXLIV. 

1.  How  many  gills  in  1  pt  ?  In  2  pints  ?  In  1  quart  ? 

2.  How  many  pints  in  2  quarts  ?  In  3  qt.  ?  In  1  gal.  ? 

3.  How  many  pints  in  £  gal.  ?  In  f  gal.  ?  In  1£  gal.  ? 
^.  How  many  gallons  in  12  quarts  ?  In  24  qt.?  In  36  ? 
J.  How  many  quarts  in  10  pints  ?  18  pt.  ?  In  20  pt.  ? 
£.  How  many  pints  in  4  qt.  1  pt.  ?     In  6  qt.  1  pt.  ? 
7.  In  1  pint,  how  many  fluid-ounces  ?     In  2  pints  ? 
6*.  How  many  quarts  in  1  peck  ?     In  3  pk.  ? 

9.  How  many  pints  in  1  pk.  ?     In  1  pk.  1  qt.  ? 

10.  How  many  quarts  in  £  bushel  ?     In  |  bushel  ? 

11.  How  many  pecks  in  2  bushels?  In  l£bu.?  In  2Jbu.? 

12.  How  many  half-pecks  in  a  bushel  ?     In  2  bu.  ? 
7#.  In  48  quarts,  how  many  pecks  ?     How  many  bu.  ? 
14-  In  64  pints,  how  many  quarts  ?    pecks  ?    bushels  ? 
^5.  When  milk  is  worth  10  cents  a  quart,  what  is  a 

pint  worth  ?     What  is  1  gallon  worth  ? 

16.  At  5  cents  a  pint,  what  will  a  half -peck  of  chest- 
nuts cost  ?     3  qt.  1  pt.  ? 

17.  How  many  pounds  in  a  half-bushel  of  wheat  ?     In 
\  bu.  of  corn  ?     In  \  bu.  of  oats  ? 

18.  How  many  pounds  in  a  peck  of  oats  ?     Of  barley  ? 

19.  At  4  cents  a  pint,  what  will  2  quarts  of  milk  cost  ? 

20.  If  a  cup  hold  3  pints,  how  many  times  can  you  fill 
it  from  a  3  gallon  jar  full  of  water  ? 

21.  If  a  bushel  of  plums  cost  2  dollars,  what  is  the 
cost  of  a  peck  ?     Of  a  quart  ? 

22.  How  many  quart  boxes  will  3  pk.  6  qt.  of  berries 
fill  ?     How  many  half -gallon  measures  ? 


ABITHMETIC. 


159 


LESSON    CXLV. 

1.  Troy   Weight  is  used  in  weighing  gold,  silver, 
and  jewels,  and  in  philosophical  experiments. 


TABLE. 

24  Grains  (gr.)      =  1  Pennyweight     .  pwt. 
20  Pennyweights  =  1  Ounce  .     .     .     .  oz. 
12  Ounces  —  1  Pound  .  .  Ib. 


(  5760  gr. 
.  -  1    240  pwt. 
(     12  oz. 


Ib  1  = 


2.  Apothecaries9  Weight  is  used  by  apothecaries 
and  physicians  in  compounding  dry  medicines. 

20  Grains  (gr.  xx)  =  1  Scruple  .  sc.,  or  3. 

3  Scruples  (3  iij)  =  1  Dram  .  dr.,  or  3. 

8  Drams  (  3  viij)  —  1  Ounce  .  oz.t  or  §  . 

12  Ounces  (  §  xij)  =  1  Pound  .  Ib.,  or  ft  . 

Medicines  are  bought  and  sold  in  quantities  by  Avoirdupois 
weight. 

The  pound,  ounce  and  grain  are  the  same  as  those  of  Troy 
weight,  the  ounce  being  differently  divided. 


160  FIRST     BOOK 


LESSON    CXLVI. 

1.  Avoirdtipois  Weight  is  used  for  all  the  ordi- 
nary purposes  of  weighing. 

TABLE. 

16  Ounces  (02.)       =  1  Pound  .     .     .     .  Ib.  /  32000  02. 

100  Pounds              =  1  Hundredweight    cwt.    1  T.  =  J    2000  Ib. 
20  cwt.,  or20001b.=  1  Ton T.  ")        20  cwt 

The  ounce  is  often  divided  into  halves,  quarters,  etc. 

2.  The  following  denominations  are  also  used  : 

100  Pounds  of  Grain  or  Flour  make  1  Cental. 
100  Pounds  of  Dry  Fish  "       1  Quintal. 

100  Pounds  of  Nails  "       1  Cask  or  Keg. 

190  Pounds  of  Flour  "      1  Barrel. 

200  Pounds  of  Pork  or  Beef       '•      1  Barrel. 

3.  COMPAKATIVE   T^BLE   OF   WEIGHTS. 

Troy.  Avoirdupois.  Apothecaries'. 

1  Pound  =  5760  Grains,    =  7000  Grains,    =  5760  Grains. 
1  Ounce  =480       "         =    437.5     "        =480 

175  Pounds,  =    144  Pounds,  =    175  Pounds. 

The  Standard  Bushel  of  the  United  States  contains  2150.42  cubie 
inches,  and  is  a  cylindrical  measure  18  J-  inches  in  diameter  and  8 
inches  deep. 

The  English  Quarter  contains  8  Imp.  bushels,  or  8|  U.  S.  bushels. 

Grain  is  shipped  from  New  York  by  the  Quarter  of  480  Ib.  (8 
U.  S.  bu.),  or  by  the  ton  of  33 \  U.  S.  bushels. 

It  is  sufficiently  accurate  in  practice  to  call  5  stricken  measures 
equal  to  4  heaped  measures. 

The  Standard  Liquid  Gallon  of  the  United  States  contains  231 
cubic  inches,  and  is  equal  to  about  8J  Ib.  Avoir,  of  pure  water. 

The  half-peck,  or  dry  gallon,  contains  268.8  cubic  inches. 

Six  dry  gallons  are  equal  to  nearly  seven  liquid  gallong. 


IN     ARITHMETIC.  161 

LESSON    CXLVII. 

1.  How  many  ounces  in  2  pounds  of  tea  ?    In  3  Ib.  ? 

2.  How  many  pennyweights  in  two  ounces  ?     Ounces 
in  60  pwt.  ?     Pounds  in  48  ounces  ? 

3.  How  many  drams  in  1  ounce  ?  In  3  ?  In  4  ?  In  6  ? 

4.  How  many  ounces  in  |  a  pound  ?     In  £  ?     In  f  ? 

5.  How  many  pounds  in  a  hundredweight  ?  In  3  cwt.? 

6.  How  many  pounds  in  1|  cwt.  ?  In  2|  cwt.  ?  In  %  cwt.? 

7.  How  many  hundred  weight  in  1  ton  ?     In  2  tons  ? 
In  I  ton?    In-J?     In  f  ? 

8.  How  many  ounces  in  1  pound  of  gold  chain  ?     In 
1  pound  of  medicine  ?     In  1  pound  of  coffee  ? 

9.  At  6  cents  a  pound,  how  many  pounds  of  rice  can 
you  buy  for  30  cents  ?     For  42  cents  ? 

10.  In  2  cwt.  40  lb.,  how  many  pounds?  In  5  cwt.  50  To.? 

11.  What  part  of  a  hundredweight  are  50  pounds  ? 
Are  25  pounds  ?    Are  75  pounds  ? 

12.  How  many  hundredweight  in  £  of  a  ton  of  hay  ? 
In  -J-  of  a  ton  ?    In  ^  of  a  ton  ? 

13.  How  many  pounds  in  %  barrel  of  pork  ?    In  -J-  bar- 
rel of  beef  ?     In  -J-  barrel  of  flour  ? 

14.  At  9  cents  a  pound,  what  will  a  keg  of  nails  cost  ? 

15.  At  2  cents  a  pound,  what  will  a  cental  of  flour  cost  ? 

16.  What  will  5  centals  of  wheat  cost,  at  4  dollars  a 
cental  ?     6  centals,  at  3  dollars  a  cental  ? 

17.  How  many  barrels  are  600  pounds  of  pork  ? 

18.  How  many  centals  are  500  pounds  of  flour  ? 

19.  How  many  kegs  are  800  pounds  of  nails  ? 

20.  How  many  barrels  are  1000  pounds  of  beef? 


162 


FIRST     BOOK 


LESSON    CXLVIII. 

1.  Time  is  the  measure  of  a  portion  of  duration. 
TABLE. 

60  Seconds  (sec.)  —  1  Minute  .  .  mm 

60  Minutes  =  1  Hour    .  .  .  hr. 

24  Hours  =  1  Day      .  .  .  da. 

1  Days  =  1  Week  .  .  .  tafc. 

365  Days,  or         ) 


COMMON  YEAR. 

(  525600  min. 
8760  hr. 


1  Yr.  = 


] 


12  mo. 
365  da. 


[  =  1  Common  Year.  yr. 
12  Calendar  Mo.  J  L 

366  Days  =  1  Leap  Year.    .    yr. 

2.  Circular    or  Angular   Measure  is  used  in 
measuring  angles,  ares  of  circles,,  etc. 
TABLE. 

60  Seconds  (/;)       =  1  Minute     .    .     .    ' 
60  Minutes  =  1  Degree     .     .    . 

30  Degrees  —  1  Sign    .     .     .     .    8. 

12  Signs,  or  360°  =  1  Circle      .     .     .     C. 

A  Semi-  Circumference  is  one-half  of  a  circumference,  or  180°. 

A  Quadrant  is  one-fourth  of  a  circumference,  or  90°. 

A  Sign  is  one-twelfth  of  a  circumference,  or  30°. 

A  Degree  (1°)  is  one-thirtieth  of  a  Sign. 


10.= 


1296000". 
21600'. 
360D. 
12  & 


ARITHMETIC. 


163 


LESSON    CXLIX. 

1.  Certain  classes  of  articles  for  market  purposes  are 
counted. 


12  Units   =  1  Dozen    .    . 

12  Dozen  —  1  Gross     .     . 

12  Gross    —  1  Great  Gross 

20  Units    =  1  Score 


TABLE. 

.  doz. 

.  gro. 

.  G.  gro. 

.  sc. 


t  1728  units. 
1  G.  gro.  =  -J    144  doz. 
(      12  gro. 


Two  things  of  a  kind  are  often  called  a  pair,  and  six  things  a  set ; 
as  a  pair  of  horses,  a  set  of  chairs,  etc. 


The  paper  trade  use  the  following  : 


24  Sheets     = 

20  Quires     = 

2  Reams    = 

5  Bundles  = 


1  Quire 
1  Ream 
1  Bundle 
1  Bale  . 


qr. 
rm. 
bun. 
B. 


4800  Sheets. 
200  Quires. 
10  Reams. 
5  Bundles. 


Paper  is  bought  at  wholesale  by  the  bale,  bundle,  and  ream  ;  and 
at  retail  by  the  ream,  quire,  and  sheet. 


164 


FIBST     BOOK 


LESSON    CL. 

Name  the  months  in  the  year,  and  the  number  of  days 
in  each. 


MONTHS. 

No.  DAYS. 

MONTHS. 

No 

DATS. 

1. 

January, 

Jan., 

31  , 

7. 

July, 

July, 

31 

2. 

February, 

Feb., 

28  or  2fj 

8. 

August, 

Aug., 

31 

3. 

March, 

Mar., 

31 

9. 

September, 

Sept., 

30 

4. 

April, 

Apr., 

30 

10. 

October, 

Oct., 

31 

5. 

May, 

May, 

31 

11. 

November, 

N<n>., 

30 

6. 

June, 

June, 

30 

12. 

December, 

Dec., 

31 

A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 
A  sheet  of  paper  folded  in 


BOOKS. 

2  leaves  is  called  a  folio. 

4  leaves  is  called  a  quarto,   or  4to. 

8  leaves  is  called  an  octavo,  or  8w. 
12  leaves  is  called  a  duodecimo,  or  12mo. 
16  leaves  is  called  a  16 mo. 
18  leaves  is  called  an  18mo. 
24  leaves  is  called  a  Ql^mo. 
32  leaves  is  called  a  32mo. 


MONEY    MENTIONED    IN    THE    BIBLE. 


A  Talent  (gold) 
A  Talent  (silver) 
A  Mancli  or  Mina 
A  Pound  (Mina) 
A  Shekel  (gold) 
A  Shekel  (silver) 
A  Golden  Daric  or  Dram 
A  Piece  of  Silver  (Stater) 
Tribute  Money  (Didrachm) 
A  Bekah 

A  Piece  of  Silver  (Drachm) 
A  Penny  (Denarius) 
.  A  Farthing  ( Assarium) 
A  Mite 


value  in  U.  S.  Money,     $26593.809 
1602.024 

11  27.699 

15.715 
8.861 
0.547 
5.312 
0.628 

"  "         "  0.314 

0.263 
0.157 
0.152 

"  "         "  0.008 

"          "         "  0.002 


IN     ARITHMETIC.  165 

LESSON    CLI. 

1.  How  many  days  in  1  week  ?    In  3  wk.  ?   In  4  wk.  ? 

2.  How  many  hours  in  £  of  a  day  ?     In  J  ?     In  f  ? 
8.  How  many  minutes  in  |  of  an  hour  ?   In  J?   In  £  ? 

4.  How  many  months  in  %  of  a  year  ?    In  £  ?     In  f  ? 

5.  How  many  days  has  a  leap  year  ? 

6.  How  often  does  leap  year  occur  ? 

7.  Name  the  months  of  the  year. 

8.  Name  the  months  that  have  30  da.  each.     31  da. 

9.  What  month  is  it  now  ?     How  many  days  has  it  ? 

10.  How  many  days  from  April  20th  to  May  10th. 

11.  How  many  days  from  Aug.  1st  to  Sept.  5th. 

12.  How  many  buttons  in  1  gross  ?     In  -|  of  a  gross  ? 

13.  How  many  pens  in  J  of  a  gross  ?  How  many  dozen  ? 
H.  Find  the  cost  of  -J  of  a  gross  of  eggs,  at  20  cents  a 

dozen. 

15.  How  many  make  1  pair  ?     2}  pairs  ?     5  pairs  ? 

16.  How  many  in  1  set  ?    In  J  a  set  ?    In  2|  set  ? 

17.  How  many  quires  of  paper  in  ^  of  a  ream  ? 

18.  How  many  sheets  of  paper  in  2  quires  ?     In  -J-  of 
a  quire  ? 

19.  Find  the  cost  of  £  of  a  ream  of  paper,  at  20  cents 
a  quire. 

#0.  How  many  score  in  40  ?     In  60  ?     In  100  ? 
#./.  How  many  in  £  of  a  score  ?  In  1£  score  ?   2£  score  ? 
22.  Which  is  greater,  £  of  a  ream  or  100  sheets  of  paper  ? 
£2.  What  is  the  difference  between  J-  of  a  dozen,  and  6 
dozen  eggs  ? 
&£.  Which  is  greater,  6  sets  of  chairs,  or  2£  dozen  chairs? 


166  FIRST     BOOK 

LESSON    CLII. 

1.  What  is  the  difference  in  a  foot  long  and  a  foot 
square  ?    In  a  square  foot  and  a  cubic  foot  ? 

2.  How  many  inches  long  is  a  block  in  the  form  of  a 
cubic  foot  ?    How  many  wide  ? 

8.  What  is  measured  by  the  fathom  ?    By  the  hand  ? 

4.  How  many  feet  deep  is  a  river  that  measures  5 
fathoms  ? 

5.  How  many  feet  high  is  a  horse  that  measures  15 
hands  ? 

6.  How  many  square  feet  in  a  blackboard  27  ft.  long 
and  3  ft.  wide  ?     How  many  square  yards  ? 

7.  Which  is  greater,  10  square  inches  or  a  10  inch 
square  ? 

8.  Which  is  greater,  6  cubic  inches  or  a  6  inch  cube  ? 

9.  How  many  squares,  each  equal  to  a  square  foot, 
are  equal  to  a  surface  12  ft.  long  and  8  ft.  wide  ? 

10.  How  many  cubes,  each  equal  to  a  cubic  foot,  are 
equal  to  a  block  5  ft.  long,  4  ft.  wide,  and  3  ft.  thick  ? 

1 L  How  is  stone  measured  ?    How  is  wood  measured  ? 

12.  Give  the  dimensions  of  a  cord-foot. 

IS.  How  many  pints  of  water  will  fill  a  vessel  that 
holds  1£  gallons  ? 

14.  How  many  times  can  a  peck  measure  be  filled  from 
2i  bushels  ? 

15.  Which  is  heavier,  a  bushel  of  wheat  or  a  bushel  of 
corn  ?    A  bushel  of  barley  or  a  bushel  of  oats  ? 

16.  Which  is  heavier,  a  barrel  of  flour  or  a  barrel  of 
pork  ?    A  keg  of  nails  or  a  cental  of  grain  ? 


ARITHMETIC. 


167 


LESSON     CLI. 

ROMAN     NOTATION. 

1.  This  method  employs  seven  capital  letters  to  repre- 
sent numbers. 

LETTEKS.    I,      V,      X,      L,      C,      D,      M. 

VALUES.     1,       5,       10,      50,     100,    500,    1000. 

#.  Eepeating  a  letter  repeats  its  value. 
Thus,  XX  represents  20  ;  CCC,  300  ;  DD,  1000. 

3.  When  a  letter  is  placed  after  one  of  greater  value, 
its  value  is  to  be  added  to  that  of  the  greater. 

Thus,  VI  represents  6  ;   XV,  15  ;  LXX,  70  ;  DC,  600. 

4.  When  a  letter  is  placed  before  one  of  greater  value, 
its  value  is  taken  from  that  of  the  greater. 

Thus,  IV  represents  4 ;   IX,  9  ;  XL,  40 

TABLE  OF  ROMAN  NOTATION. 


I 

=    1 

XIV 

=      14 

LX 

60 

II 

=      2 

XV 

=      15 

LXX 

=       70 

III 

=      3 

XVI 

=      16 

LXXX 

=       80 

IV 

=      4 

XVII 

=      17 

XC 

=        90 

V 

=      5 

XVIII 

=      18 

C 

=      100 

VI 

=      6 

XIX 

=      19 

CXIX 

=      119 

VII 

=      7 

XX 

=      20 

CC 

=      200 

VIII 

=      8 

XXI 

=      21 

ccx 

=      210 

IX 

=      9 

XXV 

=      25 

D 

=      500 

X 

=    10 

XXX 

=      30 

DCV 

=      605 

XI 

=    11 

XXXIV 

=      34 

M 

=    1000 

XII 

=    12 

XL 

=      40 

MDL 

=    1550 

XIII 

=    13 

L 

=      50 

MDCLXVI 

=    1666 

MDCCCLXXV=1875,  one  thousand  eight  hundred  and  seventy-five. 


168 


FIRST     BOOK. 


MULTIPLICATION  TABLE. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

33 

36 

4 

8 

12. 

16 

20 

24 

28 

32 

36 

40 

44 

48 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60  i 

6 

12 

18 

24 

30 

36 

42 

48 

54 

60 

66 

72 

7 

14 

21 

28 

35 

42 

49 

56 

63 

70 

77 

84 

8 

16 

24 

32 

40 

48 

56 

64 

72 

80 

88 

96 

9 

18 

27 

36 

45 

54 

63 

72 

81 

90 

99 

108 

1O 

20 

30 

40 

50 

60 

70 

80 

90 

100 

110 

120 

11 

22 

33 

44 

55 

66 

77 

88 

99 

110 

121 

132 

12 

24 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 

i  1 

13 

14 

15 

ie!i7 

18|19 

2O  2l'22 

23J24 

2 

20 

23 

30 

32;  34  36 

38 

40|  42 

44 

46 
69 
92 
115 

48 

_i?! 
96 

120 

3 

4 

39 

42 

45 

60 

48 

51 

54 

57 

eo 

~80 
100 

63 

66 

52 

56 

64 

80 

68 

72 

76 

84  88 

5 

65 

70 

75 

85 

90 

95 

105 

110 

6 

78 

84 

90 

96 
112 

102 
119 

108 

114 

i-?o 

126 

132 

138 

144 

7 

91 

98 

105 

126 

133 

140 

147 

154 

161 

168 

8 

104 

112 

120 

128*136 

144 
162 

152 

160 

168 

176 

184 

192 

216! 

9 

117 

126 

135 

144 

153 

171180189 

198 

207 

10 

130 

140 

150 

160 

170 

187 

180 
198 
216 

190 
209 
228 

200 
220 
240 

210 

220 

230 

240 

264 

ill 

143 

154 

165 

176 

231 

242 

253 

12 

156 

16g 

180 

192  204 

252 

264 

276 

288 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 


